A tightness property of relatively smooth permutations

Abstract

It is well known that many geometric properties of Schubert varieties of type $A$ can be interpreted combinatorially. Given two permutations $w,x\in S_n$ we give a combinatorial consequence of the property that the smooth locus of the Schubert variety $X_w$ contains the Schubert cell $Y_x$. This is a necessary ingredient for the interpretation of recent representation-theoretic results of the author with Mínguez in terms of identities of Kazhdan--Lusztig polynomials.

References in corpus (1)

• Geometric conditions for $\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field

Cited by in corpus (3)

• Geometric conditions for $\square$-irreducibility of certain representations of the general linear group over a non-archimedean local field
• Conjectures about certain parabolic Kazhdan--Lusztig polynomials
• Some combinatorial results on smooth permutations