EISENSTEIN SERIES AND QUANTUM AFFINE ALGEBRAS

A recent paper on the topic is Travkin. Post as a guest Name. References Publications referenced by this paper. The one closest to your question is in the direct line of Kapranov’s very influential paper. Showing of 40 references. MathOverflow works best with JavaScript enabled. Unfortunately not that much is written about quantum geometric Langlands — its origins are in works of Feigin-Frenkel and Beilinson-Drinfeld, and the idea has been around since the late 90s, but it’s hard to find in the literature until recently though see the withdrawn preprint by Stoyanovsky , still available on arXiv in early versions, for the general idea.

By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of service , privacy policy and cookie policy , and that your continued use of the website is subject to these policies. The topic of Hall algebras is extremely active I recommend Schiffmann’s beautiful survey. Gerhard Ringel Plant Roots. But maybe this response is not the right place to survey what this conjecture is actually about.. Arkhipov-Bezrukavnikov-Ginzburg and other [amazing] papers of Bezrukavnikov, but this is in a somewhat different direction, though of course everything is related. In any case a major paper on this topic is Gaitsgory’s paper constructing quantum groups directly out of a deformed version of the geometric Satake correspondence. Unfortunately not that much is written about quantum geometric Langlands — its origins are in works of Feigin-Frenkel and Beilinson-Drinfeld, and the idea has been around since the late 90s, but it’s hard to find in the literature until recently though see the withdrawn preprint by Stoyanovsky , still available on arXiv in early versions, for the general idea. Showing of 40 references.

References Publications referenced by this paper.

There are various close connections between undeformed, plain old geometric Langlands and quantum groups as well, see e. Have other authors come at this, perhaps from other perspectives? Showing of 40 references.

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Poisson Lie groups, quantum duality principle and…. Post as a guest Name. But maybe this response is not the right place to survey what this algebrzs is actually about. Sign up or log in Sign up using Google. The topic of Hall algebras is extremely active I recommend Schiffmann’s beautiful survey.

Algebraic Geometry

Post Your Answer Discard By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. The Hecke operators on functions on moduli spaces of bundles are a part of the multiplication action of the Hall algebra of this category on itself, and if we replace functions with sheaves study Hall categories we recover the basic questions in eisensgein function field version of the theory quanutm automorphic forms.

Convolution Pointwise mutual information Parabolic antenna Vertex. The subject got a major push from the fact that it arises very naturally from the gauge theory point of view on geometric Langlands due to Kapustin-Witten.

Skip to search form Skip to main content. David Feldman David Feldman 8, 6 51 In any case a major paper on this topic is Gaitsgory’s paper constructing quantum groups directly out of a deformed version of the geometric Satake correspondence.

Citations Publications citing this paper. By clicking “Post Your Answer”, you acknowledge that you have read our updated terms of serviceprivacy policy and cookie policyand that your continued use of the website is subject to these policies. Poisson Lie groups, quantum duality principle and affihe quantum double, Contemporary math.

Eisenstein Series and Quantum Affine Algebras

The one closest to your question is in the direct line of Kapranov’s very influential paper. Email Required, but never shown. The paper Eisenstein series and quantum affine algebras by Kapranov makes contact between automorphic forms and quantum groups. Gerhard Ringel Plant Roots.

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A Guide to Quantum groups. Showing of 21 citations. Algeebras using our site, you acknowledge that you have read and understand our Cookie PolicyPrivacy Policyand our Terms of Service. Unfortunately not that much is written about quantum geometric Langlands — its origins are in works of Feigin-Frenkel and Beilinson-Drinfeld, and the idea has been around since the late 90s, but it’s hard to find in anv literature until recently though see the withdrawn preprint by Stoyanovskystill available on arXiv in early versions, for the general idea.

Eisenstein Series and Quantum Affine Algebras – Semantic Scholar

Home Questions Tags Users Unanswered. MathOverflow works best with JavaScript enabled. Hall algebras, hereditary algebras and quantum groups. On the other hand, since Kapranov’s paper in particular there’s been affine realization that the quantim geometric Langlands program for general linear groups is a subset of the study of the [categorified] theory of Hall algebras – namely the case of Hall algebras for categories of coherent sheaves on curves.

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Sign up using Facebook. Drinfeld double and Green-Ringel theory of Hall algebras. There are innumerable papers this relates to, but I eisentsein the most directly relevant to your question are the wonderful papers of Schiffmann and Vasserot on Hall algebras, Macdonald polynomials, geometric Eisenstein series and geometric Langlands see arXiv search for those two names.

Drinfeld realization of the elliptic Hall algebra Olivier Schiffmann

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