Permutations *w* in *Sn* for which the (type-A) Schubert variety Ω*w* is smooth are characterized by avoidance of the patterns 3412 and 4231. The smaller family of codominant permutations, those avoiding the pattern 312, seems to explain a lot about character evaluations at Kazhdan-Lusztig basis elements *C'w(q)* of the (type-A) Hecke algebra. In particular, for every Hecke algebra character χ, and every 3412-, 4231-avoiding permutation *w*, there exists a codominant permutation *v* such that χ(*C'w(q)*) = χ(*C'v(q)*). Moreover, these character evaluations can be computed by playing simple games with unit interval orders *P* = *P(v)* corresponding to the codominant permutations. We generalize these facts to the hyperoctahedral group *Bn* using signed pattern avoidance and an appropriate analog of unit interval orders.

### CAGE: Philadelphia Area Combinatorics and Alg. Geometry Seminar

Thursday, October 19, 2023 - 3:30pm

#### Mark Skandera

Lehigh