Finite Reflection Groups (Graduate Texts in Mathematics, 99)

Finite Reflection Groups (Graduate Texts in Mathematics)

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Finite Reflection Groups (Graduate Texts in Mathematics, 99)

Finite Reflection Groups (Graduate Texts in Mathematics)

Written by Larry C. Grove
4.85 63,656 ratings
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Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are geo- metrically indistinguishable, that is, conjugate in the orthogonal group. Very little of the material in Chapter 2 is actually required for the sub- sequent chapters, but it serves two important purposes: It aids in the development of geometrical insight, and it serves as a source of illustrative examples. There is a discussion offundamental regions in Chapter 3. Chapter 4 provides a correspondence between fundamental reflections and funda- mental regions via a discussion of root systems. The actual classification and construction of finite reflection groups takes place in Chapter 5. where we have in part followed the methods of E. Witt and B. L. van der Waerden. Generators and relations for finite reflection groups are discussed in Chapter 6. There are historical remarks and suggestions for further reading in a Post lude.

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Pages N/A
Published 1971
ISBN 3892030
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About the Author
Larry C. Grove

After spending years working in the corporate world, Larry C. Grove finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Mary Evans
Mary Evans September 15, 2024
A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Brian Young
Brian Young August 13, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Patricia Hernandez
Patricia Hernandez August 10, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Sharon Rivera
Sharon Rivera February 23, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Susan King
Susan King April 09, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Joshua Jackson September 22, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Sharon Nguyen June 21, 2024
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Carol Williams
Carol Williams October 30, 2025
A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Donna Ramirez
Donna Ramirez February 16, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Andrew Harris
Andrew Harris May 10, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Emily Thompson
Emily Thompson October 11, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Karen Hall
Karen Hall May 25, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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Jennifer Hall August 10, 2024
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Barbara Phillips
Barbara Phillips April 04, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Elizabeth Jones
Elizabeth Jones June 22, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Joseph Scott
Joseph Scott January 20, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Elizabeth Perez
Elizabeth Perez April 15, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Gary Hernandez
Gary Hernandez July 01, 2024
An acceptable diversion. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Margaret Taylor
Margaret Taylor May 04, 2024
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Sarah Cruz
Sarah Cruz November 26, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Sarah Cruz
Sarah Cruz January 20, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Matthew Diaz
Matthew Diaz July 17, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Patricia Smith
Patricia Smith December 01, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Joseph Thompson
Joseph Thompson September 28, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
William Taylor
William Taylor May 27, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Michael Collins
Michael Collins August 02, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Christopher Rodriguez
Christopher Rodriguez February 27, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
George Green
George Green July 13, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Lisa Gomez
Lisa Gomez August 08, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Rebecca Wilson
Rebecca Wilson February 14, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Gary Reyes
Gary Reyes June 09, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
Edward Allen
Edward Allen August 11, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Amanda Johnson
Amanda Johnson December 15, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Jennifer Robinson
Jennifer Robinson March 21, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Margaret Walker
Margaret Walker November 28, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Jennifer Hall
Jennifer Hall November 24, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Elizabeth Collins
Elizabeth Collins March 02, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Ryan Collins
Ryan Collins June 01, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Steven Lee
Steven Lee March 20, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
George Turner
George Turner July 24, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Donald Torres
Donald Torres March 22, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Emily Diaz
Emily Diaz November 28, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Barbara Hill
Barbara Hill February 23, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Christopher Wright
Christopher Wright April 14, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Gary Hernandez
Gary Hernandez April 05, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Laura Torres
Laura Torres November 25, 2025
It was adequate. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
Melissa Moore
Melissa Moore April 07, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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