Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$

Ben Cox; Vyacheslav Futorny; Kailash C. Misra

Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$

Quantum Algebra 2013-08-16 v2 Representation Theory

Authors: Ben Cox , Vyacheslav Futorny , Kailash C. Misra

Abstract

We consider imaginary Verma modules for quantum affine algebra $U_q(\hat{\mathfrak{g}})$ , where $\hat{\mathfrak{g}}$ is of type 1 i.e. of non-twisted type, and construct Kashiwara type operators and the Kashiwara algebra $\mathcal K_q$ . We show that a certain quotient $\mathcal N_q^-$ of $U_q(\hat{\mathfrak{g}})$ is a simple $\mathcal K_q$ -module.

Keywords

quantum affine algebra imaginary Verma modules Kashiwara algebra Kashiwara operators non-twisted type simple module

Cite

@article{arxiv.1308.1974,
  title  = {Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$},
  author = {Ben Cox and Vyacheslav Futorny and Kailash C. Misra},
  journal= {arXiv preprint arXiv:1308.1974},
  year   = {2013}
}

Comments

arXiv admin note: substantial text overlap with arXiv:1307.2941

Kashiwara Algebras and Imaginary Verma Modules for $U_q(\hat{\mathfrak{g}})$

Abstract

Keywords

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