کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8895790 1630403 2018 26 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Representations of quantum groups at roots of unity, Whittaker vectors and q-W algebras
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Representations of quantum groups at roots of unity, Whittaker vectors and q-W algebras
چکیده انگلیسی
Let Uε(g) be the standard simply connected version of the Drinfeld-Jumbo quantum group at an odd m-th root of unity ε. The center of Uε(g) contains a huge commutative subalgebra isomorphic to the algebra ZG of regular functions on (a finite covering of a big cell in) a complex connected, simply connected algebraic group G with Lie algebra g. Let V be a finite-dimensional representation of Uε(g) on which ZG acts according to a non-trivial character ηg given by evaluation of regular functions at g∈G. Then V is a representation of the finite-dimensional algebra Uηg=Uε(g)/Uε(g)Kerηg. We show that in this case, under certain restrictions on m, Uηg contains a subalgebra Uηg(m−) of dimension m12dimO, where O is the conjugacy class of g, and Uηg(m−) has a one-dimensional representation Cχg. We also prove that if V is not trivial then the space of Whittaker vectors HomUηg(m−)(Cχg,V) is not trivial and the algebra Wηg=EndUηg(Uηg⊗Uηg(m−)Cχg) naturally acts on it which gives rise to a Schur-type duality between representations of the algebra Uηg and of the algebra Wηg called a q-W algebra.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 511, 1 October 2018, Pages 63-94
نویسندگان
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