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Representations of Rational Cherednik Algebras in Positive Characteristic

- Martina Balagovic, H. Chen
- Mathematics
- 3 July 2011

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 Cherednik… Expand

19 5- PDF

Universal K-matrix for quantum symmetric pairs

- Martina Balagovic, S. Kolb
- Mathematics, Physics
- 22 July 2015

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 pair… Expand

45 3- PDF

Irreducible representations of the rational Cherednik algebra associated to the Coxeter group H_3

- Martina Balagovic, Arjun Puranik
- Mathematics
- 13 April 2010

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 the… Expand

13 3- PDF

Degeneration of Trigonometric Dynamical Difference Equations for Quantum Loop Algebras to Trigonometric Casimir Equations for Yangians

- Martina Balagovic
- Mathematics
- 10 August 2013

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 to… Expand

7 2- PDF

On the lower central series quotients of a graded associative algebra

- Martina Balagovic, A. Balasubramanian
- Mathematics
- 21 April 2010

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

13 2- PDF

Category O for rational Cherednik algebras Ht,c(GL2(Fp),h) in characteristic p

- Martina Balagovic, H. Chen
- Mathematics
- 29 July 2011

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

5 1- PDF

Translation functors and decomposition numbers for the periplectic Lie superalgebra $\mathfrak{p}(n)$

- Martina Balagovic, Z. Daugherty, +7 authors C. Stroppel
- Mathematics
- 26 October 2016

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 with… Expand

19- PDF

On representations of quantum groups and Cherednik algebras

- Martina Balagovic
- Mathematics
- 2011

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, the… Expand

Translation functors and Kazhdan--Lusztig multiplicities for the Lie superalgebra $\mathfrak{p}(n)$

- Martina Balagovic, Z. Daugherty, +7 authors C. Stroppel
- Mathematics
- 26 October 2016

Chevalley restriction theorem for vector-valued functions on quantum groups

- Martina Balagovic
- Mathematics
- 2 April 2010

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 when… Expand

5- PDF

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