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
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
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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 gâG. 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(mâ) of dimension m12dimO, where O is the conjugacy class of g, and Uηg(mâ) has a one-dimensional representation CÏg. We also prove that if V is not trivial then the space of Whittaker vectors HomUηg(mâ)(CÏg,V) is not trivial and the algebra Wηg=EndUηg(UηgâUηg(mâ)CÏg) 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
Journal: Journal of Algebra - Volume 511, 1 October 2018, Pages 63-94
نویسندگان
A. Sevostyanov,