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arXiv · 1203.5590

Crystal bases of q-deformed Kac modules over the quantum superalgebra $U_q(\gl(m|n))$

Jae-Hoon Kwon
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Abstract

We introduce the notion of a crystal base of a finite dimensional q-deformed Kac module over the quantum superalgebra $U_q(\gl(m|n))$, and prove its existence and uniqueness. In particular, we obtain the crystal base of a finite dimensional irreducible $U_q(\gl(m|n))$-module with typical highest weight. We also show that the crystal base of a q-deformed Kac module is compatible with that of its irreducible quotient $V(λ)$ given by Benkart, Kang and Kashiwara when $V(λ)$ is an irreducible polynomial representation.

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BibTeXRIS

Jae-Hoon Kwon. 2012-04-23. Crystal bases of q-deformed Kac modules over the quantum superalgebra $U_q(\gl(m|n))$. https://arxiv.org/abs/1203.5590

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