Imaginary Verma Modules for U_q(\widehat\mathfraksl(2)) and Crystal-like bases

2015/09/02 by Ben Cox, Vyacheslav Futorny, Cox, Ben +4
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #math.RT

paper · pdf · doi:10.48550/arxiv.1509.00865

arXiv admin note: text overlap with arXiv:0903.1062

arxiv created 2015/09/02 · arxiv updated 2015/09/04

Abstract

We consider imaginary Verma modules for quantum affine algebraU_q(\widehat\mathfraksl(2)) and define a crystal-like base which we call an imaginary crystal basis using the Kashiwara algebra K_q constructed in earlier work of the authors. In particular, we prove the existence of imaginary like bases for a suitable category of reduced imaginary Verma modules for U_q(\widehat\mathfraksl(2)).

Citations

• Imaginary Verma modules and Kashiwara algebras for U_q(\widehat\mathfraksl(2))

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