An algebraic approach to the KZ-functor for rational Cherednik algebras associated with cyclic groups

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• 作者：Sam Thelin¹ ; ^{sam.thelin@mathematik.uni-stuttgart.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：16G99
• 刊名：Journal of Algebra
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：471
• 期：Complete
• 页码：113-148
• 全文大小：688 K

文摘

We give a complete algebraic description of the KZ-functor for rational Cherednik algebras associated with cyclic groups for a subset of parameter values from which all parameter values can be obtained by integral translations. This is done by identifying the precise parameter values for which the projective object class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303222&_mathId=si1.gif&_user=111111111&_pii=S0021869316303222&_rdoc=1&_issn=00218693&md5=87e8865fcad5280f068560666b642b7a" title="Click to view the MathML source">P_KZclass="mathContainer hidden">class="mathCode">$P_{\mathrm{KZ}}$ is isomorphic to the Δ-module associated with the coinvariant algebra and by determining the action of the cyclotomic Hecke algebra on class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0021869316303222&_mathId=si1.gif&_user=111111111&_pii=S0021869316303222&_rdoc=1&_issn=00218693&md5=87e8865fcad5280f068560666b642b7a" title="Click to view the MathML source">P_KZclass="mathContainer hidden">class="mathCode">$P_{\mathrm{KZ}}$ in this case.