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- W1669982445 abstract "Let $K$ be a field and $qin K^{times}$. Let $e$ be the multiplicative order of $q$; or 0 if $q$ is not a root of unity. Let $bQ:=(q^{v_1},...,q^{v_r})$. Let ${K}_r(n)$ be the set of Kleshchev $r$-multipartitions with respect to $(e;bQ)$. In this paper, we consider an extention of Dipper--James--Murphy's Conjecture to the Ariki--Koike algebra $H_{r,n}(q;bQ)$ with $r>2$. We show that any $(bQ,e)$-restricted $r$-multipartition of $n$ is a Kleshchev multipartition in ${K}_r(n)$; and if $e>1$, then any multi-core $ulam=(lam^{(1)},...,lam^{(r)})$ in ${K}_r(n)$ is a $(bQ,e)$-restricted $r$-multipartition. As a consequence, we show that if $e=0$ (i.e., $q$ is not a root of unity), then ${K}_r(n)$ coincides with the set of $(bQ,e)$-restricted $r$-multipartitions of $n$ and also coincides with the set of ladder $r$-multipartitions of $n$." @default.
- W1669982445 created "2016-06-24" @default.
- W1669982445 creator A5045858327 @default.
- W1669982445 date "2009-02-14" @default.
- W1669982445 modified "2023-09-22" @default.
- W1669982445 title "On a generalization of Dipper--James--Murphy's Conjecture" @default.
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- W1669982445 hasPublicationYear "2009" @default.
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