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Quantum symmetric Kac–Moody pairs
The present paper develops a general theory of quantum group analogs of symmetric pairs for involutive automorphism of the second kind of symmetrizable Kac–Moody algebras. The resulting quantumExpand
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De Rham complex for quantized irreducible flag manifolds
It is shown that quantized irreducible flag manifolds possess a canonical q-analogue of the de Rham complex. Generalizing the well-known situation for the standard Podleś' quantum sphere thisExpand
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The Locally Finite Part of the Dual Coalgebra of Quantized Irreducible Flag Manifolds
For quantized irreducible flag manifolds the locally finite part of the dual coalgebra is shown to coincide with a natural quotient coalgebra $\overline{U}$ of $U_q ( \mathfrak{g} )$. On the way theExpand
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Braid group action and root vectors for the $q$-Onsager algebra
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 toExpand
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Braided module categories via quantum symmetric pairs
  • S. Kolb
  • Mathematics, Physics
  • 11 May 2017
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 monoidalExpand
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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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On the Bernstein-Gelfand-Gelfand Resolution for Kac-Moody Algebras and Quantized Enveloping Algebras
A Bernstein-Gelfand-Gelfand resolution for arbitrary Kac-Moody algebras and arbitrary subsets of the set of simple roots is proven. Moreover, quantum group analogs of the Bernstein-Gelfand-GelfandExpand
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Right coideal subalgebras of the Borel part of a quantized enveloping algebra
For the Borel part of a quantized enveloping algebra, we classify all right coideal subalgebras for which the intersection with the coradical is a Hopf algebra. The result is expressed in terms ofExpand
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Radial Part Calculations for ŝl2 and the Heun-KZB Heat Equation
In the present paper, we determine the radial part of the Casimir element for the affine Lie algebra ŝl2 with respect to the Chevalley involution. The resulting operator is identified with a blend ofExpand
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Braid group actions on coideal subalgebras of quantized enveloping algebras
Abstract We construct braid group actions on coideal subalgebras of quantized enveloping algebras which appear in the theory of quantum symmetric pairs. In particular, we construct an action of theExpand
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