The Action of the Hall-littlewood Vertex Operator
نویسنده
چکیده
The vertex operators Hm act on the Hall-Littlewood polynomials HX; t] with the property that HmHX; t] = H (m;;) X; t]. We present a combinatorial rule for computing the action of Hm on the schur function basis which interpolates the Pieri formula for multiplication by hmX] and the schur function vertex operator. This rule suggests the existence of an operator on column strict tableaux of content that produces tableaux of content (m + jj;). The operator on tableaux can be deened in terms of Lascoux and Sch utzenberger's Jeu de Taquin and gives as a result a new formula for H (m;;) X; t] as a weighted sum over tableaux of content (m + jj;). It is shown that cancellation in this formula reduces to H (m;;) X; t] as a weighted sum over tableaux of content (m;).
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