A Littlewood-Richardson rule for the Macdonald inner product and bimodules over wreath products

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• 作者：Erik Carlsson ; ^{carlsson@cmsa.fas.harvard.edu" class="auth_mail" title="E-mail the corresponding author} ; Anthony M. Licata
• 关键词：Littlewood Richardson ; Categorification ; Wreath products ; Symmetric functions ; Macdonald inner product ; Quantum algebra ; Combinatorics
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 May 2016
• 年：2016
• 卷：454
• 期：Complete
• 页码：520-537
• 全文大小：370 K

文摘

We prove a Littlewood–Richardson type formula for (s_λ/μ,s_ν/κ)_t^k,t${(s_{\lambda /\mu },s_{\nu /\kappa })}_{t^k,t}$, the pairing of two skew Schur functions in the Macdonald inner product at q=t^k$q=t^k$ for positive integers k  . This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra C[x]/x^k$\mathbb{C}[x]/x^k$ and symmetric groups.