Rogers-Ramanujan type identities and Nil-DAHA

被引：21
作者：
Cherednik, Ivan [1 ]
Feigin, Boris [2 ,3 ,4 ]
机构：
[1] UNC, Dept Math, Chapel Hill, NC 27599 USA
[2] Natl Res Univ, Higher Sch Econ, Moscow 101000, Russia
[3] LD Landau Theoret Phys Inst, Chernogolovka 142432, Russia
[4] Independent Univ Moscow, Moscow 119002, Russia
来源：
ADVANCES IN MATHEMATICS | 2013年 / 248卷
基金：
美国国家科学基金会;
关键词：
Rogers-Ramanujan identities; Hecke algebras; q-Hermite polynomials; Dilogarithm; Kac-Moody algebras; Demazure characters; Modular functions; Coset algebras; CONFORMAL FIELD-THEORIES; DILOGARITHM IDENTITIES; MACDONALD POLYNOMIALS; WEYL MODULES; T-SYSTEMS; ALGEBRAS; REPRESENTATIONS; PERIODICITIES; CONJECTURE; MODEL;
D O I：
10.1016/j.aim.2013.08.025
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Using the DAHA-Fourier transform of q-Hermite polynomials multiplied by level-one theta functions, we obtain expansions of products of any number of such theta functions in terms of the q-Hermite polynomials. An ample family of modular functions satisfying Rogers-Ramanujan type identities for arbitrary (reduced, twisted) affine root systems is obtained as an application. A relation to Rogers dilogarithm and Nahm's conjecture is discussed. The q-Hermite polynomials are closely related to the Demazure level-one characters in the twisted case (Sanderson, Ion), which connects our formulas to tensor products of level-one integrable Kac-Moody modules, their coset theory and the level-rank duality. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：1050 / 1088
页数：39
相关论文
共 52 条
  • [1] Al-Salam W.A., 1984, PAC J MATH, V114, P267
  • [2] Andrews G.E., 1988, PAC J MATH, V135, P209
  • [3] Andrews G.E., 1998, THEORY PARTITIONS
  • [4] [Anonymous], 2002, Kac-Moody Groups, Their Flag Varieties and Their Representations
  • [5] Bennett M., ARXIV12072446MATHRT
  • [6] Bourbaki N., 1969, GROUPES ALGEBRES LIE
  • [7] Cherednik I, 1997, INT MATH RES NOTICES, V1997, P449
  • [8] Cherednik I., 2006, LONDON MATH SOC LECT, V319
  • [9] Cherednik I., 1995, Int. Math. Res. Not., V10, P483, DOI [DOI 10.1155/S1073792895000341, 10.1155/S1073792895000341]
  • [10] One-dimensional nil-DAHA and Whittaker functions II
    Cherednik, Ivan
    Orr, Daniel
    [J]. TRANSFORMATION GROUPS, 2013, 18 (01) : 23 - 59
123456