Workshop on "Algebra and Geometry of Configuration Spaces and related structures" June 21th through 25th

Lower intervals in the Bruhat order and inversion arrangements

speaker: John Shareshian (Washington University in St. Louis)

abstract: Abstract: In joint work with A. Hultman, S. Linusson and J. Sj\"ostrand, we proved the following conjecture of A. Postnikov. Let w be an element of the symmetric group S_n. Let A_w be the arrangement of those hyperplanes in Rⁿ defined by the equations x_i=xj whenever (i,j) is an inversion of w. Then

(1) The number of regions in the complement of A_w is at most the number of elements below w in the Bruhat order, and

(2) equality holds in (1) if and only if w avoids a fixed (finite and known) set of patterns.

I will describe in some detail our proof of (1), which works for any finite Coxeter group. I will discuss some aspects of (2) if time permits.

timetable:
Mon 21 Jun, 16:15 - 17:15, Aula Dini
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