Zobrazeno 1 - 10
of 237
pro vyhledávání: '"P. Baseilhac"'
We prove that the quantum moduli algebra associated to a possibly punctured compact oriented surface and a complex semisimple Lie algebra $\mathfrak{g}$ is a Noetherian and finitely generated ring; if the surface has punctures, we prove also that it
Externí odkaz:
http://arxiv.org/abs/2302.00396
We study universal solutions to reflection equations with a spectral parameter, so-called K-operators, within a general framework of universal K-matrices - an extended version of the approach introduced by Appel-Vlaar. Here, the input data is a quasi
Externí odkaz:
http://arxiv.org/abs/2301.00781
Autor:
Baseilhac, Pascal, Pimenta, Rodrigo A.
The $q$-Racah polynomials are expressed in terms of certain ratios of scalar products of Bethe states associated with Bethe equations of either homogeneous or inhomogeneous type. This result is obtained by combining the theory of Leonard pairs and th
Externí odkaz:
http://arxiv.org/abs/2211.14727
Autor:
Baseilhac, Pascal
Publikováno v:
Nuclear Physics B 975 (2022) 115682
A unified framework for the Chevalley and equitable presentation of $U_q(sl_2)$ is introduced. It is given in terms of a system of Freidel-Maillet type equations satisfied by a pair of quantum K-operators ${\mathcal K}^\pm$, whose entries are express
Externí odkaz:
http://arxiv.org/abs/2106.11715
Autor:
Baseilhac, Pascal
Publikováno v:
Lett. Math. Phys. 112 2 (2022)
The equitable presentation of the quantum algebra $U_q(\widehat{sl_2})$ is considered. This presentation was originally introduced by T. Ito and P. Terwilliger. In this paper, following Terwilliger's recent works the (nonstandard) positive part of $U
Externí odkaz:
http://arxiv.org/abs/2106.11706
Autor:
Baseilhac, Stéphane, Roche, Philippe
Publikováno v:
SIGMA 20 (2024), 047, 70 pages
We prove that the quantum graph algebra and the quantum moduli algebra associated to a punctured sphere and complex semisimple Lie algebra $\mathfrak{g}$ are Noetherian rings and finitely generated rings over $\mathbb{C}(q)$. Moreover, we show that t
Externí odkaz:
http://arxiv.org/abs/2106.04136
Autor:
Baseilhac, Pascal
An infinite dimensional algebra denoted $\bar{\cal A}_q$ that is isomorphic to a central extension of $U_q^+$ - the positive part of $U_q(\widehat{sl_2})$ - has been recently proposed by Paul Terwilliger. It provides an `alternating' Poincar\'e-Birkh
Externí odkaz:
http://arxiv.org/abs/2011.01572
Akademický článek
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Autor:
Baseilhac, Stéphane, Roche, Philippe
Publikováno v:
SIGMA 18 (2022), 025, 78 pages
Let $\Sigma$ be a finite type surface, and $G$ a complex algebraic simple Lie group with Lie algebra $\mathfrak{g}$. The quantum moduli algebra of $(\Sigma,G)$ is a quantization of the ring of functions of $X_G(\Sigma)$, the variety of $G$-characters
Externí odkaz:
http://arxiv.org/abs/1912.02440
Autor:
Baseilhac, Pascal, Pimenta, Rodrigo A.
An operator of Heun-Askey-Wilson type is diagonalized within the framework of the algebraic Bethe ansatz using the theory of Leonard pairs. For different specializations and the generic case, the corresponding eigenstates are constructed in the form
Externí odkaz:
http://arxiv.org/abs/1909.02464