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Canonical bases for the quantum linear supergroups (1410.0757v2)
Published 3 Oct 2014 in math.QA, math.GR, math.RA, and math.RT
Abstract: We give a combinatorial construction for the canonical bases of the $\pm$-parts of the quantum enveloping superalgebra $\bfU(\mathfrak{gl}{m|n})$ and discuss their relationship with the Kazhdan-Lusztig bases for the quantum Schur superalgebras $\bsS(m|n,r)$ introduced in \cite{DR}. We will also extend this relationship to the induced bases for simple polynomial representations of $\bfU(\mathfrak{gl}{m|n})$.