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Эта публикация цитируется в 5 научных статьях (всего в 5 статьях)
On unitary submodules in the polynomial representations of rational Cherednik algebras
M. Feigina, C. Shramovb a School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow G12 8QW, UK
b Steklov Mathematical Institute, Gubkina str., 8, Moscow 119991, Russia
Аннотация:
We consider representations of rational Cherednik algebras that are particular ideals in the ring of polynomials. We investigate convergence of the integrals that express the Gaussian inner product on these representations. We derive that the integrals converge for the minimal submodules in types $B$ and $D$ for the singular values suggested by Cherednik with at most one exception; hence the corresponding modules are unitary. The analogous result on unitarity of the minimal submodules in type $A$ was obtained by Etingof and Stoica; we give a different proof of convergence of the Gaussian product in this case. We also obtain partial results on unitarity of the minimal submodule in the case of exceptional Coxeter groups and group $B$ with unequal parameters.
Поступила в редакцию: 29.10.2010 Исправленный вариант: 18.04.2011 Принята в печать: 21.06.2011
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