Separable elements and splittings in Weyl groups of Type B

2023/09/06 by Liu, Ming, Yu, Houyi · 1 citation
#05E16 #06A11 #20F55 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2309.02932

Abstract

Separable elements in Weyl groups are generalizations of the well-known class of separable permutations in symmetric groups. Gaetz and Gao showed that for any pair (X,Y) of subsets of the symmetric group \mathfrakS_n, the multiplication map X× Y→ \mathfrakS_n is a splitting (i.e., a length-additive bijection) of \mathfrakS_n if and only if X is the generalized quotient of Y and Y is a principal lower order ideal in the right weak order generated by a separable element. They conjectured this result can be extended to all finite Weyl groups. In this paper, we classify all separable and minimal non-separable signed permutations in terms of forbidden patterns and confirm the conjecture of Gaetz and Gao for Weyl groups of type B.

Cited by

• Combinatorial equivalence of separable elements in types A and B

Related

• Combinatorial equivalence of separable elements in types A and B
• Casselman--Shahidi conjecture on the singularity of intertwining operators: groups of exceptional type
• Intervals and factors in the Bruhat order
• Twisted conjugacy and separability
• Separators - a new statistic for permutations