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Hyperoctahedral group characters and a type-BC chromatic symmetric function

Algebra & Discrete Mathematics

Speaker: Mark Skandera, Lehigh University
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Location: 2112 MSB
Start time: Tue, Feb 20 2024, 1:10PM

If $w$ in the symmetric group $S_n$ avoids the patterns $3412$ and $4231$, then we may graphically represent the Kazhdan-Lusztig basis element $\widetilde C_w \in \mathbb Z[S_n]$ by an indifference graph $G = G(w)$. The evaluations of certain characters at $\widetilde C_w$ then appear as coefficients in expansions of Stanley's chromatic symmetric function $X_G$. For $w$ in the hyperoctahedral group $B_n$ avoiding the same patterns, we define a type-BC indifference graph $G = G(w)$ which graphically represents the Kazhdan-Lusztig basis element $\widetilde C_w \in \mathbb Z[B_n]$. We also define a type-BC chromatic symmetric function $X_G$ whose coefficients record character evaluations at this basis element.