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 g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869315002975&_mathId=si1.gif&_user=111111111&_pii=S0021869315002975&_rdoc=1&_issn=00218693&md5=dc155f759a04251ece83bfbd5e5d3749" title="Click to view the MathML source">(s_λ/μ,s_ν/κ)_t^k,tgif" overflow="scroll">(sλ/μ,sν/κ)tk,t, the pairing of two skew Schur functions in the Macdonald inner product at g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869315002975&_mathId=si2.gif&_user=111111111&_pii=S0021869315002975&_rdoc=1&_issn=00218693&md5=1ea91ab09bd4c0a62f8c463477fd935b" title="Click to view the MathML source">q=t^kgif" overflow="scroll">q=tk for positive integers k  . This pairing counts graded decomposition numbers in the representation theory of wreath products of the algebra g" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869315002975&_mathId=si3.gif&_user=111111111&_pii=S0021869315002975&_rdoc=1&_issn=00218693&md5=58895dea442594c16560c34139ce7504" title="Click to view the MathML source">C[x]/x^kgif" overflow="scroll">C[x]/xk and symmetric groups.