Regularity of quantum tau-functions generated by quantum birational Weyl group actions

2012/06/15 by Gen Kuroki, Kuroki, Gen
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT

paper · pdf · doi:10.48550/arxiv.1206.3419

28 pages

openalex publication_date 2012/06/15 · arxiv created 2014/06/23 · arxiv updated 2014/06/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We canonically quantize the tau-functions for the birational Weyl group action arising from a nilpotent Poisson algebra proposed by Noumi and Yamada. We also construct the q-difference deformation of the canonical quantization of the tau-functions. Using the translation functors for the symmetrizable Kac-Moody algebras, we prove the regularity of the quantum tau-functions, namely, we show that the quantum tau-functions are polynomials in dependent variables.

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