# Questions tagged [schubert-varieties]

The tag has no usage guidance.

11 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
164 views

### Are Schubert varieties for Kac-Moody groups cut out by linear equations?

Let $G$ be a reductive group, and let $X$ be a partial flag variety for $G$. Then it is known that for any projective embedding of $X$, that the equations scheme-theoretically cutting out a Schubert ...
92 views

### Richardson variety over arbitrary field

Let $G$ be a split semisimple algebraic group. Let $B$ and $T$ be borel subgroup ,maximal torus respectively. In this case the Weyl group $W(B,T)$ is a constant finite group scheme. Let $P$ be a ...
I have two questions concerning morphism between local cohomology groups which I think are related. Let $G$ be a reductive group with Weyl group $W$ and $B \subset G$ a Borel. Let $X=G/B$ be the flag ...
Let $(W,S)$ be a Coxeter system with length function $\ell$ and $T=\bigcup_{w\in W}wSw^{-1}$. Set $N(u,v):=\{t\in T: u< tu \le v\}$, $\overline{\ell}(u,v):=|N(u,v)|$, $\ell(u,v):=\ell(v)-\... 3 votes 0 answers 117 views ### Non-generic intersections of Schubert varieties? Let$G$be a linear algebraic group,$B$a Borel subgroup,$P$a parabolic subgroup containing$B$, and$W$the Weyl group. For$w \in W$, the Schubert variety$X_w^P$is the closure of the Schubert ... 3 votes 0 answers 487 views ### Schubert varieties of flag variety , perverse sheaves The set of Schubert varieties in a flag variety is in one-to-one correspondence with elements of the Weyl group via left cells. There is also some relation between products of Schubert varieties and ... 1 vote 0 answers 100 views ### Bruhat decomposition and standard Frobenius Let$G$be a linear algebraic group define over$\overline{\mathbb{F}_p}$, consider it as a subgroup of$\operatorname{GL}(n)$. Let$F_p$be the standard Frobenius. Let$B$and$Q$be an$F_p$-stable ... 1 vote 0 answers 50 views ### Is the complement of an$\epsilon$-neighborhood an affinoid open polydisc in a flag variety?$\newcommand{\rig}{\mathrm{rig}}$Let$K$be non-Archimedean local field of characteristic zero with non-Archimedean norm$|\,\,|$(assumed to be normalised), ring of integer$\mathcal{O}_K$and$C$, ... 1 vote 0 answers 83 views ### Spaces intersecting a plane non-trivially in$G(3,6)$I want to understand the Schubert variety$\Sigma\subseteq G(3,6)$representing 3-dim subspaces intersecting a given 2-dim subspace non-trivially. Is it smooth? How to describe$det(T_{\Sigma})$? 1 vote 1 answer 416 views ### On some notations and notions of a paper on smoothness of Schubert varieties by Lakshmibai and Sandhya I am reading the paper Criterion for smoothness of Schubert varieties in$\mathrm{Sl}(n)/B$by V Lakshmibai and B Sandhya; Proc. Indian Acad. Sci. (Math. Sci.), Vol. 100, No. 1, April 1990, pp. 45-52. ... 1 vote 1 answer 184 views ### Coefficients of the monomials appearing in a Schubert polynomial It is known that the coefficients of the monomials appearing in a Schubert polynomial are always positive. My question is: Is it always true that at least one such coefficient must be$1\$? If that is ... 