Candidate for the crystal $B(-\infty )$ for the queer Lie superalgebra

Abstract

It is shown that the direct limit of the semistandard decomposition tableau model for polynomial representations of the queer Lie superalgebra exists, which is believed to be the crystal for the upper half of the corresponding quantum group. An extension of this model to describe the direct limit combinatorially is given. Furthermore, it is shown that the polynomial representations may be recovered from the limit in most cases.

arXiv comment25 pages, 3 figures

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Cited by in corpus (2)

• Crystal base of the negative half of the quantum superalgebra $U_q(\mathfrak{gl}(m|n))$
• Crystal bases of parabolic Verma modules over the quantum orthosymplectic superalgebras