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arXiv · 1808.09388

Canonical bases for tensor products and super Kazhdan-Lusztig theory

Huanchen Bao·Weiqiang Wang·Hideya Watanabe
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Abstract

We generalize a construction in [BW18] (arXiv:1610.09271) by showing that the tensor product of a based $\textbf{U}^{\imath}$-module and a based $\textbf{U}$-module is a based $\textbf{U}^{\imath}$-module. This is then used to formulate a Kazhdan-Lusztig theory for an arbitrary parabolic BGG category $\mathcal{O}$ of the ortho-symplectic Lie superalgebras, extending a main result in [BW13] (arXiv:1310.0103).

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Huanchen Bao, Weiqiang Wang, Hideya Watanabe. 2018-08-28. Canonical bases for tensor products and super Kazhdan-Lusztig theory. https://doi.org/10.1007/s00222-018-0801-5

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