richardson variety
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2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Edward Richmond ◽  
Vasu Tewari ◽  
Stephanie Van Willigenburg

International audience The geometric Littlewood-Richardson (LR) rule is a combinatorial algorithm for computing LR coefficients derived from degenerating the Richardson variety into a union of Schubert varieties in the Grassmannian. Such rules were first given by Vakil and later generalized by Coskun. In this paper we give a noncommutative version of the geometric LR rule. As a consequence, we establish a geometric explanation for the positivity of noncommutative LR coefficients in certain cases.


2019 ◽  
Vol 19 (10) ◽  
pp. 2050186
Author(s):  
Arpita Nayek ◽  
S. K. Pattanayak

For any simple, simply connected algebraic group [Formula: see text] of type [Formula: see text] and [Formula: see text] and for any maximal parabolic subgroup [Formula: see text] of [Formula: see text], we provide a criterion for a Richardson variety in [Formula: see text] to admit semistable points for the action of a maximal torus [Formula: see text] with respect to an ample line bundle on [Formula: see text].


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