Demazure Character Formulas for Generalized Kac--Moody Algebras

2013/04/14 by Motohiro Ishii, Ishii, Motohiro
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1304.3867

openalex publication_date 2013/04/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a dominant integral weight lambda , we introduce a family of U_q ⁺ (mathfrakg)-submodules V_w (lambda) of the irreducible highest weight U_q (mathfrakg)-module V(lambda) of highest weight lambda for a generalized Kac--Moody algebra mathfrakg. We prove that the module V_w (lambda) is spanned by its global basis, and then give a character formula for V_w (lambda), which generalizes the Demazure character formula for ordinary Kac--Moody algebras.

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