Tensor product decompositions for cohomologies of Bott-Samelson varieties

Abstract

Let $T$ be a maximal torus of a semisimple complex algebraic group, $\mathrm{BS}(s)$ be the Bott-Samelson variety for a sequence of simple reflections $s$ and $\mathrm{BS}(s{)}^T$ be the set of $T$-fixed points of $\mathrm{BS}(s)$. We prove the tensor product decompositions for the image of the restriction $H_T^{\bullet }(\mathrm{BS}(s),k)\to H_T^{\bullet }(X,k)$, where $X\subset \mathrm{BS}(s{)}^T$ is defined by some special not overlapping equations ${\gamma }_i{\gamma }_{i+1}\cdots {\gamma }_j=w_{i,j}$ with right-hand sides belonging to the Weyl group.

arXiv admin note: text overlap with arXiv:2006.00551

References in corpus (1)

• The T-equivariant Cohomology of Bott-Samelson varieties