论文信息 - Quantum Queer Superalgebra and Crystal Bases

Quantum Queer Superalgebra and Crystal Bases

In this paper, we develop the crystal basis theory for the quantum queer superalgebra $\Uq$. We define the notion of crystal bases, describe the tensor product rule, and present the existence and uniqueness of crystal bases for finite-dimensional $\Uq$-modules in the category $\mathcal{O}_{int}^{\ge 0}$.

[1] A. Sergeev. Representations of the Lie superalgebras gl (n, m) and Q(n) on the space of tensors , 1984 .

[2] Masaki Kashiwara,et al. Crystalizing theq-analogue of universal enveloping algebras , 1990 .

[3] M. Kashiwara,et al. On crystal bases of the $Q$-analogue of universal enveloping algebras , 1991 .

[4] Masaki Kashiwara,et al. Crystal Graphs for Representations of the q-Analogue of Classical Lie Algebras , 1994 .

[5] V. Serganova,et al. Characters of Finite-Dimensional Irreducible q(n) -Modules , 1997 .

[6] Masaki Kashiwara,et al. Crystal Bases for the Quantum Superalgebra $U_q(gl(m,n))$ , 1998 .

[7] Masaki Kashiwara,et al. Crystal bases for the quantum superalgebra _ , 2000 .

[8] Ji Hye Jung,et al. Highest Weight Modules over Quantum Queer Superalgebra U Q (q(n)) , 2009 .