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# Documents  20G43 | enregistrements trouvés : 3

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## Recent advances in representation theory, quantum groups, algebraic geometry, and related topics.AMS special sessions on geometric and algebraic aspects of representation theory and quantum groups and noncommutative algebraic geometryNew Orleans # october 13-14, 2012 Achar, Pramod N. ; Jakelic, Dijana ; Misra, Kailash C. ; Yakimov, Milen | American Mathematical Society 2014

Congrès

- x; 280 p.
ISBN 978-0-8218-9852-9

Contemporary mathematics , 0623

Localisation : Collection 1er étage

représentation de groupe # groupe quantique # géométrie algébrique # physique mathématique # théorie des représentations # algèbre de Kac-Moody # superalgèbre de Lie # algèbre toroïdale # algèbre de Leibniz

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## A new spectral theory for Schur polynomials and applications Moll, Alexander | CIRM H

Multi angle

Research schools;Combinatorics;Dynamical Systems and Ordinary Differential Equations

After Fourier series, the quantum Hopf-Burgers equation $v_t +vv_x = 0$ with periodic boundary conditions is equivalent to a system of coupled quantum harmonic oscillators, which may be prepared in Glauber's coherent states as initial conditions. Sending the displacement of each oscillator to infinity at the same rate, we (1) confirm and (2) determine corrections to the quantum-classical correspondence principle. After diagonalizing the Hamiltonian with Schur polynomials, this is equivalent to proving (1) the concentration of profiles of Young diagrams around a limit shape and (2) their global Gaussian fluctuations for Schur measures with symbol $v : T \to R$ on the unit circle $T$. We identify the emergent objects with the push-forward along $v$ of (1) the uniform measure on $T$ and (2) $H^{1/2}$ noise on $T$. Our proofs exploit the integrability of the model as described by Nazarov-Sklyanin (2013). As time permits, we discuss structural connections to the theory of the topological recursion. After Fourier series, the quantum Hopf-Burgers equation $v_t +vv_x = 0$ with periodic boundary conditions is equivalent to a system of coupled quantum harmonic oscillators, which may be prepared in Glauber's coherent states as initial conditions. Sending the displacement of each oscillator to infinity at the same rate, we (1) confirm and (2) determine corrections to the quantum-classical correspondence principle. After diagonalizing the ...

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## Weighted Schur algebras or "Diagrammatic Cherednik algebras" over fields of arbitrary characteristic Bowman, Christopher David | CIRM H

Multi angle

Research talks;Algebra

We begin by introducing to the diagrammatic Cherednik algebras of Webster. We then summarise some recent results (in joint work with Anton Cox and Liron Speyer) concerning the representation theory of these algebras. In particular we generalise Kleshchev-type decomposition numbers, James-Donkin row and column removal phenomena, and the Kazhdan-Lusztig approach to calculating decomposition numbers.

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