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比利时vs摩洛哥足彩 ,
university of california san diego

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math 269 - combinatorics seminar

raymond chou

uc davis

a descent basis for the garsia-procesi module

abstract:

the garsia-procesi module $r_\lambda$ has a well known basis of artin monomials indexed by λ-subyamanouchi words, which correspond to the inv-statistic of the haglund-haiman-loehr combinatorial formula for the modified macdonald polynomials $h_\lambda(x;q,t)$ at $t=0$. we introduce a new basis for $r_\lambda$ of garsia-stanton descent monomials, giving a major-index type formula of the modified hall-littlewood polynomial $h_\lambda(x;q,t)$, and discuss the subtle connection to $h_\lambda(x;q,t)$ at $q=0$ via robinson-schensted-knuth insertion. our formula was discovered while searching for a basis of the garsia-haiman module by extending a similar result of carlsson and oblomkov for the diagonal coinvariants $dh_n$. this is joint work with e. carlsson.

host: brendon rhoades

november 7, 2022

4:00 pm

apm 5402

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