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Author : Catherine E. Kriloff
Release : 1995
Genre :
Kind : eBook
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Book Synopsis Representations of Graded Hecke Algebras Associated to Noncrystallographic Root Systems by : Catherine E. Kriloff
Download or read book Representations of Graded Hecke Algebras Associated to Noncrystallographic Root Systems written by Catherine E. Kriloff. This book was released on 1995. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nanhua Xi
Release : 1994-09-26
Genre : Mathematics
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Book Synopsis Representations of Affine Hecke Algebras by : Nanhua Xi
Download or read book Representations of Affine Hecke Algebras written by Nanhua Xi. This book was released on 1994-09-26. Available in PDF, EPUB and Kindle. Book excerpt: Kazhdan and Lusztig classified the simple modules of an affine Hecke algebra Hq (q E C*) provided that q is not a root of 1 (Invent. Math. 1987). Ginzburg had some very interesting work on affine Hecke algebras. Combining these results simple Hq-modules can be classified provided that the order of q is not too small. These Lecture Notes of N. Xi show that the classification of simple Hq-modules is essentially different from general cases when q is a root of 1 of certain orders. In addition the based rings of affine Weyl groups are shown to be of interest in understanding irreducible representations of affine Hecke algebras. Basic knowledge of abstract algebra is enough to read one third of the book. Some knowledge of K-theory, algebraic group, and Kazhdan-Lusztig cell of Cexeter group is useful for the rest
Author : Ivan Cherednik
Release : 2005-03-24
Genre : Mathematics
Kind : eBook
Book Rating : 254/5 ( reviews)
Book Synopsis Double Affine Hecke Algebras by : Ivan Cherednik
Download or read book Double Affine Hecke Algebras written by Ivan Cherednik. This book was released on 2005-03-24. Available in PDF, EPUB and Kindle. Book excerpt: This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Physics, and Combinatorics. It is a major source of general information about the double affine Hecke algebra, also called Cherednik's algebra, and its impressive applications. Chapter 1 is devoted to the Knizhnik-Zamolodchikov equations attached to root systems and their relations to affine Hecke algebras, Kac-Moody algebras, and Fourier analysis. Chapter 2 contains a systematic exposition of the representation theory of the one-dimensional DAHA. It is the simplest case but far from trivial with deep connections in the theory of special functions. Chapter 3 is about DAHA in full generality, including applications to Macdonald polynomials, Fourier transforms, Gauss-Selberg integrals, Verlinde algebras, and Gaussian sums. This book is designed for mathematicians and physicists, experts and students, for those who want to master the double Hecke algebra technique. Visit http://arxiv.org/math.QA/0404307 to read Chapter 0 and selected topics from other chapters.
Author : George Lusztig
Release : 2003
Genre : Mathematics
Kind : eBook
Book Rating : 561/5 ( reviews)
Book Synopsis Hecke Algebras with Unequal Parameters by : George Lusztig
Download or read book Hecke Algebras with Unequal Parameters written by George Lusztig. This book was released on 2003. Available in PDF, EPUB and Kindle. Book excerpt: Hecke algebras arise in representation theory as endomorphism algebras of induced representations. One of the most important classes of Hecke algebras is related to representations of reductive algebraic groups over $p$-adic or finite fields. In 1979, in the simplest (equal parameter) case of such Hecke algebras, Kazhdan and Lusztig discovered a particular basis (the KL-basis) in a Hecke algebra, which is very important in studying relations between representation theory and geometry of the corresponding flag varieties. It turned out that the elements of the KL-basis also possess very interesting combinatorial properties. In the present book, the author extends the theory of the KL-basis to a more general class of Hecke algebras, the so-called algebras with unequal parameters. In particular, he formulates conjectures describing the properties of Hecke algebras with unequal parameters and presents examples verifying these conjectures in particular cases. Written in the author's precise style, the book gives researchers and graduate students working in the theory of algebraic groups and their representations an invaluable insight and a wealth of new and useful information.
Author : David A. Nash
Release : 2010
Genre : Hecke algebras
Kind : eBook
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Book Synopsis Graded Representation Theory of Hecke Algebras by : David A. Nash
Download or read book Graded Representation Theory of Hecke Algebras written by David A. Nash. This book was released on 2010. Available in PDF, EPUB and Kindle. Book excerpt:
