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arXiv · 2308.16254

Canonical bases via pairing monomials

Jonas Antor
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Abstract

For any quantum group of finite ADE type, we prove a new formula for the standard bilinear form evaluated at monomials. Combining this with ideas from the Lusztig-Shoji algorithm, we obtain a new algorithm that computes the canonical basis. In type A, the algorithm also computes composition multiplicities of standard modules for the affine Hecke algebra of $\text{GL}_n$ and we explain how the algorithm can be extended to compute the dimensions of simple modules.

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Jonas Antor. 2023-08-30. Canonical bases via pairing monomials. https://arxiv.org/abs/2308.16254

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