Combinatorics Seminar: “Combinatorial Evaluation of Hyperoctahedral Group Characters”

Speaker: Mark Skandera, Lehigh University

Abstract: For w in S_n corresponding to a smooth type-A Schubert variety X(w), there exists a poset P = P(w) which provides a combinatorial interpretation of the Kazhdan-Lusztig basis element C_w(1) in Z[S_n]. Evaluations of characters at C_w(1) may be computed by counting special P-tableaux.  We state a type-BC analog of these results. Namely, for w in the hyperoctahedral group B_n such that the type-B and type-C Schubert varieties are simultaneously smooth, there exists a type-BC poset P = P(w) which provides a combinatorial interpretation of the Kazhdan-Lusztig basis element C_w(1) in Z[B_n].

Again, evaluations of characters at the Kazhdan-Lusztig basis element C_w(1) of Z[B_n] may be computed by counting special P-tableaux.

Host: Nathan Lesnevich