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Representations of Rational Cherednik Algebras in Positive Characteristic
We study rational Cherednik algebras over an algebraically closed field of positive characteristic. We first prove several general results about category O, and then focus on rational CherednikExpand
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Universal K-matrix for quantum symmetric pairs
Let $\mathfrak{g}$ be a symmetrizable Kac-Moody algebra and let $U_q(\mathfrak{g})$ denote the corresponding quantized enveloping algebra. In the present paper we show that quantum symmetric pairExpand
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Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H_3
This paper describes irreducible representations in category O of the rational Cherednik algebra H_c(H_3,h) associated to the exceptional Coxeter group H_3 and any complex parameter c. We compute theExpand
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Degeneration of Trigonometric Dynamical Difference Equations for Quantum Loop Algebras to Trigonometric Casimir Equations for Yangians
We show that, under Drinfeld’s degeneration (Proceedings of the International Congress of Mathematicians. American Mathematical Society, Providence, pp 798–820, 1987) of quantum loop algebras toExpand
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On the lower central series quotients of a graded associative algebra
We continue the study of the lower central series Li(A) and its successive quotients Bi(A) of a noncommutative associative algebra A, defined by L1(A)=A, Li+1(A)=[A,Li(A)], and Bi(A)=Li(A)/Li+1(A).Expand
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Category O for rational Cherednik algebras Ht,c(GL2(Fp),h) in characteristic p
In this paper we describe the characters of irreducible objects in category O for the rational Cherednik algebra associated to GL2(Fp) over an algebraically closed field of positive characteristic p,Expand
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Translation functors and decomposition numbers for the periplectic Lie superalgebra $\mathfrak{p}(n)$
We study the category $\mathcal{F}_n$ of finite-dimensional integrable representations of the periplectic Lie superalgebra $\mathfrak{p}(n)$. We define an action of the Temperley--Lieb algebra withExpand
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On representations of quantum groups and Cherednik algebras
In the first part of the thesis, we study quantum groups associated to a semisimple Lie algebra g. The classical Chevalley theorem states that for [ a Cartan subalgebra and W the Weyl group of g, theExpand
Chevalley restriction theorem for vector-valued functions on quantum groups
We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan \mathfrak{h}->C. We consider the case whenExpand
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