Double Affine Hecke Algebras and Noncommutative Geometry

Double Affine Hecke Algebras and Noncommutative Geometry
Author: Alexei Oblomkov
Publisher:
Total Pages: 96
Release: 2005
Genre:
ISBN:

Download Double Affine Hecke Algebras and Noncommutative Geometry Book in PDF, Epub and Kindle

In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical subalgebra eH(t, 1)e of the Double Affine Hecke algebra H(t, 1) of type An-1 is an integral Cohen-Macaulay algebra isomorphic to the center Z of H(t, 1), and H(t, 1)e is a Cohen-Macaulay eH(t, 1)e-module with the property H(t, 1) = EndeH(t, tl)(H(t, 1)e). This implies the classification of the finite dimensional representations of the algebras. In the second part we study the algebraic properties of the five-parameter family H(tl, t2, t3, t4; q) of double affine Hecke algebras of type CVC1, which control Askey- Wilson polynomials. We show that if q = 1, then the spectrum of the center of H is an affine cubic surface C, obtained from a projective one by removing a triangle consisting of smooth points. Moreover, any such surface is obtained as the spectrum of the center of H for some values of parameters. We prove that the only fiat de- formations of H come from variations of parameters. This explains from the point of view of noncommutative geometry why one cannot add more parameters into the theory of Askey-Wilson polynomials. We also prove several results on the universality of the five-parameter family H(tl, t2, t3, t4; q) of algebras.


Double Affine Hecke Algebras and Noncommutative Geometry
Language: en
Pages: 96
Authors: Alexei Oblomkov
Categories:
Type: BOOK - Published: 2005 - Publisher:

GET EBOOK

In the first part we study Double Affine Hecke algebra of type An-1 which is important tool in the theory of orthogonal polynomials. We prove that the spherical
Double Affine Hecke Algebras
Language: en
Pages: 449
Authors: Ivan Cherednik
Categories: Mathematics
Type: BOOK - Published: 2005-03-21 - Publisher: Cambridge University Press

GET EBOOK

This is an essentially self-contained monograph centered on the new double Hecke algebra technique.
Affine Hecke Algebras and Orthogonal Polynomials
Language: en
Pages: 200
Authors: I. G. Macdonald
Categories: Mathematics
Type: BOOK - Published: 2003-03-20 - Publisher: Cambridge University Press

GET EBOOK

First account of a theory, created by Macdonald, of a class of orthogonal polynomial, which is related to mathematical physics.
Double Affine Hecke Algebras and Congruence Groups
Language: en
Pages: 90
Authors: Bogdan Ion
Categories: Education
Type: BOOK - Published: 2021-06-18 - Publisher: American Mathematical Soc.

GET EBOOK

The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data
Double Affine Hecke Algebras
Language: en
Pages: 452
Authors: Ivan Cherednik
Categories: Mathematics
Type: BOOK - Published: 2005-03-24 - Publisher: Cambridge University Press

GET EBOOK

This is an essentially self-contained monograph in an intriguing field of fundamental importance for Representation Theory, Harmonic Analysis, Mathematical Phys