Results 51 to 60 of about 307 (186)
Semiinfinite Cohomology of Quantum Groups [PDF]
Communications in Mathematical Physics, 1997 In this paper we develop a new homology theory of associative algebras called semiinfinite cohomology in a derived category setting. We show that in the case of small quantum groups the zeroth semiinfinite cohomology of the trivial module is closely related to the conformal blocks' spaces.
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Existence and orthogonality of stable envelopes for bow varieties
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3249-3306, November 2025.Abstract Stable envelopes, introduced by Maulik and Okounkov, provide a family of bases for the equivariant cohomology of symplectic resolutions. They are part of a fascinating interplay between geometry, combinatorics and integrable systems. In this expository article, we give a self‐contained introduction to cohomological stable envelopes of type A$A$
Catharina Stroppel, Till Wehrhan
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Virasoro constraints for quantum cohomology
Journal of Differential Geometry, 1998 Eguchi-Hori-Xiong and S. Katz proposed a conjecture that the partition function of topological sigma model coupled to gravity is annihilated by infinitely many differential operators which form half branch of the Virasoro algebra. In this paper, we give a proof to this conjecture for the genus 0 part.
Liu, Xiaobo, Tian, Gang
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On quantum de Rham cohomology theory [PDF]
Electronic Research Announcements of the American Mathematical Society, 1999 We define the quantum exterior product ∧ h \wedge _h and quantum exterior differential d h d_h on Poisson manifolds. The quantum de Rham cohomology, which is a deformation quantization of the de Rham cohomology, is defined as the cohomology of d h d_h
Cao, Huai-Dong, Zhou, Jian
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Remarks on some infinitesimal symmetries of Khovanov–Rozansky homologies in finite characteristic
Bulletin of the London Mathematical Society, Volume 57, Issue 11, Page 3597-3613, November 2025.Abstract We give a new proof of a theorem due to Shumakovitch and Wang on base point independence of Khovanov–Rozansky homology in characteristic p$p$. Some further symmetries of gl(p)$\mathfrak {gl}(p)$‐homology in characteristic p$p$ are also discussed.
You Qi +3 more
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Holomorphic field theories and higher algebra
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 2903-2974, October 2025.Abstract Aimed at complex geometers and representation theorists, this survey explores higher dimensional analogs of the rich interplay between Riemann surfaces, Virasoro and Kac‐Moody Lie algebras, and conformal blocks. We introduce a panoply of examples from physics — field theories that are holomorphic in nature, such as holomorphic Chern‐Simons ...
Owen Gwilliam, Brian R. Williams
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Quantum Group as Semi-infinite Cohomology [PDF]
Communications in Mathematical Physics, 2010 We obtain the quantum group $SL_q(2)$ as semi-infinite cohomology of the Virasoro algebra with values in a tensor product of two braided vertex operator algebras with complementary central charges $c+\bar{c}=26$. Each braided VOA is constructed from the free Fock space realization of the Virasoro algebra with an additional q-deformed harmonic ...
Frenkel, Igor B., Zeitlin, Anton M.
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Peterson-Lam-Shimozono’s theorem is an affine analogue of quantum Chevalley formula
Forum of Mathematics, SigmaWe give a new proof of an unpublished result of Dale Peterson, proved by Lam and Shimozono, which identifies explicitly the structure constants, with respect to the quantum Schubert basis, for the T-equivariant quantum cohomology $QH^{\bullet }_T(G/P)
Chi Hong Chow
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Entropy, 2020 In 1969, Jean-Marie Souriau introduced a “Lie Groups Thermodynamics” in Statistical Mechanics in the framework of Geometric Mechanics. This Souriau’s model considers the statistical mechanics of dynamic systems in their “space of evolution” associated to
Frédéric Barbaresco
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