Papers by David Omar Hernandez
Duke Mathematical Journal, 2015
Generalized Baxter's relations on the transfer-matrices (also known as Baxter's T Q relations) ar... more Generalized Baxter's relations on the transfer-matrices (also known as Baxter's T Q relations) are constructed and proved for an arbitrary untwisted quantum affine algebra. Moreover, we interpret them as relations in the Grothendieck ring of the category O introduced by Jimbo and the second author in [HJ] involving infinite-dimensional representations constructed in [HJ], which we call here "prefundamental". We define the transfer-matrices associated to the prefundamental representations and prove that their eigenvalues on any finite-dimensional representation are polynomials up to a universal factor. These polynomials are the analogues of the celebrated Baxter polynomials. Combining these two results, we express the spectra of the transfer-matrices in the general quantum integrable systems associated to an arbitrary untwisted quantum affine algebra in terms of our generalized Baxter polynomials. This proves a conjecture of Reshetikhin and the first author formulated in 1998 [FR1]. We also obtain generalized Bethe Ansatz equations for all untwisted quantum affine algebras. Contents 1. Introduction 2. Quantum loop algebra and Borel algebras 3. Representations of Borel algebras 4. Baxter's relations in category O 13 5. Transfer-matrices and polynomiality 18 6. A grading of positive prefundamental representations 28 7. End of the proof of Theorem 5.9 34 References 39
Mathematische Annalen, 2010
We establish a correspondence (or duality) between the characters and the crystal bases of finite... more We establish a correspondence (or duality) between the characters and the crystal bases of finite-dimensional representations of quantum groups associated to Langlands dual semi-simple Lie algebras. This duality may also be stated purely in terms of semi-simple Lie algebras. To explain this duality, we introduce an "interpolating quantum group" depending on two parameters which interpolates between a quantum group and its Langlands dual. We construct examples of its representations, depending on two parameters, which interpolate between representations of two Langlands dual quantum groups.
Letters in Mathematical Physics, 2010
We describe a correspondence (or duality) between the q-characters of finite-dimensional represen... more We describe a correspondence (or duality) between the q-characters of finite-dimensional representations of a quantum affine algebra and its Langlands dual in the spirit of [6, 4]. We prove this duality for the Kirillov-Reshetikhin modules. In the course of the proof we introduce and construct "interpolating (q, t)-characters" depending on two parameters which interpolate between the q-characters of a quantum affine algebra and its Langlands dual.
Pacific Journal of Mathematics, 2009
We begin to study the Lie theoretical analogues of symplectic reflection algebras for a finite cy... more We begin to study the Lie theoretical analogues of symplectic reflection algebras for a finite cyclic group ; we call these algebras "cyclic double affine Lie algebras". We focus on type A: In the finite (respectively affine, double affine) case, we prove that these structures are finite (respectively affine, toroidal) type Lie algebras, but the gradings differ. The case that is essentially new is sl n ([ރu, v]). We describe its universal central extensions and start the study of its representation theory, in particular of its highest weight integrable modules and Weyl modules. We also consider the first Weyl algebra A 1 instead of the polynomial ring [ރu, v], and, more generally, a rank one rational Cherednik algebra. We study quasifinite highest weight representations of these Lie algebras.
Failure analysis of a Pelton turbine manufactured in soft martensitic stainless steel casting
Engineering Failure Analysis, 2011
In this paper, the failure of a large Pelton turbine, arising immediately after receiving a quenc... more In this paper, the failure of a large Pelton turbine, arising immediately after receiving a quenching and tempering heat treatment, is analysed. The turbine was manufactured in ASTM CA-6NM soft martensitic stainless steel. A thermo-mechanical finite elements model was developed to evaluate the homogeneity of the heat treatment; for this purpose, the thermal histories of internal and external points of
Método para la extracción de ADN cloroplastídico de Bouteloua gracilis como herramienta para aplicaciones moleculares
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Papers by David Omar Hernandez