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arXiv · 1607.06033

Canonical bases of quantum Schubert cells and their symmetries

Arkady Berenstein·Jacob Greenstein
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Abstract

The goal of this work is to provide an elementary construction of the canonical basis $\mathbf B(w)$ in each quantum Schubert cell~$U_q(w)$ and to establish its invariance under modified Lusztig's symmetries. To that effect, we obtain a direct characterization of the upper global basis $\mathbf B^{up}$ in terms of a suitable bilinear form and show that $\mathbf B(w)$ is contained in $\mathbf B^{up}$ and its large part is preserved by modified Lusztig's symmetries.

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Arkady Berenstein, Jacob Greenstein. 2016-07-20. Canonical bases of quantum Schubert cells and their symmetries. https://doi.org/10.1007/s00029-017-0316-8

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