Zobrazeno 1 - 10
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pro vyhledávání: '"Kolb, Stefan A."'
Autor:
Kolb, Stefan, Stephens, Jake
We classify the finite dimensional representations of the quantum symmetric pair coideal subalgebra $B_{\mathbf c}$ of type $DII$ corresponding to the symmetric pair $(so(2N),so(2N-1))$. For $B_{\mathbf c}$ defined over an arbitrary field $k$ and $q\
Externí odkaz:
http://arxiv.org/abs/2407.15538
Autor:
Kolb, Stefan
We show that all quantum symmetric pair coideal subalgebras $B_\mathbf{c}$ of Kac-Moody type have a bar involution for a suitable choice of parameters $\mathbf{c}$. The proof relies on a generalized notion of quasi K-matrix. The proof does not involv
Externí odkaz:
http://arxiv.org/abs/2104.06120
Autor:
Kolb, Stefan, Yakimov, Milen
Publikováno v:
Forum of Mathematics, Sigma 9 (2021) e67
We explicitly determine the defining relations of all quantum symmetric pair coideal subalgebras of quantized enveloping algebras of Kac-Moody type. Our methods are based on star products on noncommutative $\mathbb{N}$-graded algebras. The resulting
Externí odkaz:
http://arxiv.org/abs/2104.05625
We introduce bivariate versions of the continuous q-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence relations) and a
Externí odkaz:
http://arxiv.org/abs/2002.07895
Publikováno v:
Proceedings of the Edinburgh Mathematical Society 63 (2020) 1092-1099
We consider the adjoint representation of a Hopf algebra $H$ focusing on the locally finite part, $H_{\text{adfin}}$, defined as the sum of all finite-dimensional subrepresentations. For virtually cocommutative $H$ (i.e., $H$ is finitely generated as
Externí odkaz:
http://arxiv.org/abs/1905.03020
Autor:
Kolb, Stefan, Yakimov, Milen
We construct symmetric pairs for Drinfeld doubles of pre-Nichols algebras of diagonal type and determine when they possess an Iwasawa decomposition. This extends G. Letzter's theory of quantum symmetric pairs. Our results can be uniformly applied to
Externí odkaz:
http://arxiv.org/abs/1901.00490
Autor:
Dobson, Liam, Kolb, Stefan
The theory of quantum symmetric pairs provides a universal K-matrix which is an analogue of the universal R-matrix for quantum groups. The main ingredient in the construction of the universal K-matrix is a quasi K-matrix which has so far only been co
Externí odkaz:
http://arxiv.org/abs/1804.02912
Autor:
Baseilhac, Pascal, Kolb, Stefan
We define two algebra automorphisms $T_0$ and $T_1$ of the $q$-Onsager algebra $B_c$, which provide an analog of G. Lusztig's braid group action for quantum groups. These automorphisms are used to define root vectors which give rise to a PBW basis fo
Externí odkaz:
http://arxiv.org/abs/1706.08747
Autor:
Kolb, Stefan
Let ${\mathfrak g}$ be a finite dimensional complex semisimple Lie algebra. The finite dimensional representations of the quantized enveloping algebra $U_q({\mathfrak g})$ form a braided monoidal category $O_{int}$. We show that the category of finit
Externí odkaz:
http://arxiv.org/abs/1705.04238
Autor:
Balagovic, Martina, Kolb, Stefan
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 coideal subalgebras $B_{c,s}$ of $U_q(\mathfrak{g})$ h
Externí odkaz:
http://arxiv.org/abs/1507.06276