Bott canonical basis?

Yael Karshon; Jihyeon Jessie Yang

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arXiv · 2106.15695

Bott canonical basis?

Yael Karshon·Jihyeon Jessie Yang

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Abstract

Expanding an idea of Raoul Bott, we propose a construction of canonical bases for unitary representations that comes from big torus actions on families of Bott-Samelson manifolds. The construction depends only on the choices of a maximal torus, a Borel subgroup ,and a reduced expression for the longest element of the Weyl group. It relies on a conjectural vanishing of higher cohomology of sheaves of holomorphic sections of certain line bundles on the total spaces of the families, hence the question mark in the title.

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Yael Karshon, Jihyeon Jessie Yang. 2021-06-29. Bott canonical basis?. https://arxiv.org/abs/2106.15695

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