The t-analog of the basic string function for twisted affine Kac-Moody algebras

2012/02/01 by Sachin S. Sharma, Sharma, Sachin S., Sankaran Viswanath +1
Mathematics · Physics and Astronomy · #17B67 #33D67 #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT #msc:17B67 #msc:33D67

paper · pdf · doi:10.48550/arxiv.1202.0118

arxiv created 2012/02/01 · openalex publication_date 2012/02/01 · arxiv updated 2012/02/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study Lusztig's t-analog of weight multiplicities associated to level one representations of twisted affine Kac-Moody algebras. An explicit closed form expression is obtained for the corresponding t-string function using constant term identities of Macdonald and Cherednik. The closed form involves the generalized exponents of the graded pieces of the twisted affine algebra, considered as modules for the underlying finite dimensional simple Lie algebra. This extends previous work on level 1 t-string functions for the untwisted simply-laced affine Kac-Moody algebras.

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