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Showing 1 to 7 of 7 for “"quantum group"”.
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Multiparameter quantum groups: contractions and coloured generalisations.
… geometric aspects of multi- parameter quantum groups. In particular, we study some two-parameter quantum groups and associated structure of Hopf algebras. We focus our attention on a new quantum group, Gr,s, depending on two deformation parameters and five generators. The first four …
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Affine quantum algebras, Weyl groups and constructible functions
… two parts. In the first part we study the affine quantum group of type A, giving a geometric description of its natural inner product, and studying the theory of cells attached to the canonical basis. In the second part we study a realization of the group algebra of the Weyl group in a convolution …
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Affine Springer fibers and the representation theory of small quantum groups and related algebras
… we study the representation theory of small quantum groups and Frobenius kernels and the geometry of an equivalued affine Springer fiber Fl[subscript ts] for s a regular semisimple element. In Chapter 2 we relate the center of the small quantum group with the cohomology of the above affine …
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Quantum intertwiners and integrable systems
… relationship between intertwining operators for quantum groups and eigenfunctions for quantum integrable systems. First, we study the Etingof-Kirillov Jr. expression of Macdonald polynomials as traces of intertwiners of quantum groups in the Gelfand-Tsetlin basis. In the quasiclassical limit, we …
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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, the restriction of g-invariant polynomials on g to [ is an isomorphism onto the W-invariant polynomials …
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Much ado about nothing: The superconformal index and Hilbert series of three dimensional N =4 vacua
We study a quantum mechanical $\sigma$-model whose target space is a hyperKähler cone. As shown by Singleton, [184], such a theory has superconformal invariance under the algebra $\mathfrak{osp}(4^*|4)$. One can formally define a superconformal index that counts the short representations of the …
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Lorentzian Poisson homogeneous spaces, quantum groups and noncommutative spacetimes
El objetivo de esta Tesis Doctoral es el estudio de ciertas deformaciones cuánticas de los grupos cinemáticos Lorentzianos (Poincaré y (anti-)de Sitter), sus espacios homogéneos cuánticos asociados, y algunas de sus consecuencias físicas. En particular, se construye el espacio no conmutativo de …