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Showing 1 to 20 of 24 for “"quantum groups"”.
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Rigid Analytic Quantum Groups
… we introduce a theory of $p$-adic analytic quantum groups. We first define Fréchet completions $\wideparen{U_q(\mathfrak{g})}$ and $\wideparen{\mathcal{O}_q(G)}$ of the quantized enveloping algebra of a semisimple Lie algebra $\mathfrak{g}$ and the quantized coordinate ring of the …
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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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Matrix valued orthogonal polynomials and quantum groups
Contains fulltext : 150268.pdf (Publisher’s version ) (Open Access)
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An introduction to the theory of quantum groups
… is meant to be an introduction to the theory of quantum groups, a new and exciting field having deep relevance to both pure and applied mathematics. Throughout the thesis, basic theory of requisite background material is developed within an overar-ching categorical framework. This background …
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Example of solvable quantum groups and their representations
Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1994.
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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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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 …
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Noncommutative Lp-spaces associated with locally compact quantum groups
Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2010-06-21T21:01:36Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Cooney_Thomas.pdf: 388303 bytes, checksum: 96eda492eeb1c47171783409857e58b8 (MD5)
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Numerical generation of semisimple tortile categories coming from quantum groups
In this work we set up a general framework for exact computations of the associativity, commutativity and duality morphisms in a quite general class of tortile categories. The source of the categories we study is the work of Gelfand and Kazhdan, Examples of tensor categories, Invent.Mlath. 109 …
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Double Crossproducts of Hopf* Algebras, Discrete Quantum Groups and Amenable Groups
… by describing a possible theory of quantum gravity where the algebra of quantum observables is a bicrossproduct.
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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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Modules over affine lie algebras at critical level and quantum groups by Qian Lin.
… a reductive Lie algebra g: the De Concini- Kac quantum algebra and the Kac-Moody Lie algebra. Recent results show that the principle block of De Concini -Kac quantum algebra at an odd root of unity with (some) fixed central character is equivalent to the core of a certain t-structure on the …
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Representation of quantum algebras arising from non-compact quantum groups : quantum orbit method and super-tensor products
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1996.
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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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Quantum stochastic flows on universal partial isometry matrix C*-algebras
We give a simple algebraic construction of quantum stochastic flows on universal C*-algebras generated by partial isometry matrix relations. This is a large class of C*-algebras that subsumes the family of graph C*-algebras and, more generally, Cuntz-Krieger algebras. The construction expands on …
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Local Structure of Operator Algebras
… provide some tools for studying locally compact quantum groups. We first consider inverse limits of $C\sp*$-algebras (pro-$C\sp*$-algebras); among them are the multipliers of the Pedersen ideal of a $C\sp*$-algebra. We distinguish these as locally compact pro-$C\sp*$-algebras and give a …
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Poisson-lie structures on infinite-dimensional jet groups and their quantization
… We construct a series of finite-dimensional quantum groups whose quasiclassical limits are finite-dimensional Poisson-Lie factor groups of G<sub>∞</sub> and G₀<sub>∞</sub>.
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Combinatorial aspects of total positivity
… positivity properties of his canonical bases for quantum groups, Lusztig extended the theory of total positivity to arbitrary reductive groups and real flag varieties. In the first part of my thesis I study the totally non-negative part of the Grassmannian and prove an enumeration theorem for a …
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EXTENDING ACTIONS OF HOPF ALGEBRAS TO ACTIONS OF THE DRINFEL'D DOUBLE
… long thought of symmetry in terms of actions of groups, but group actions have proven too restrictive in some cases to give an interesting picture of the symmetry of some mathematical objects, e.g. some noncommutative algebras. It is generally agreed that the right generalizations of group …
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Semisimple filtrations of tilting modules for algebraic groups
… the regular indecomposable tilting modules for quantum groups at roots of unity. We then show that these filtrations really do exist for these tilting modules. In the modular case, high weight tilting modules exhibit self-similarity in their characters at $p$-power scales. This is due to what we …
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