Yangians and cohomology rings of Laumon spaces

DOI10.1007/s00029-011-0059-xzbMath1260.14015arXiv0812.4656OpenAlexW2162896287MaRDI QIDQ717106

Leonid Rybnikov, Michael Finkelberg, Boris L. Feigin, Andrei Neguţ

Publication date: 27 September 2011

Published in: Selecta Mathematica. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0812.4656

zbMATH Keywords

Chern classVerma modulesYangiansuniversal enveloping algebraGelfand-Tsetlin basisparabolic sheavesGiesecker compactificationsLaumon spaces

Mathematics Subject Classification ID

Universal enveloping (super)algebras (17B35) Algebraic moduli problems, moduli of vector bundles (14D20) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43)

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Cites Work

• Unnamed Item
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• Unnamed Item
• Gelfand-Tsetlin algebras and cohomology rings of Laumon spaces
• Exts and vertex operators
• Finite difference quantum Toda lattice via equivariant \(K\)-theory
• Affine Yangians and deformed double current algebras in type \(A\)
• Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via \(K\)-theory of affine Laumon spaces
• Laumon spaces and the Calogero-Sutherland integrable system
• Vector bundles on complex projective spaces
• Un analogue global du cône nilpotent. (A global analogue of the nilpotent cone)
• Parabolic bundles as orbifold bundles
• Moduli of sheaves on surfaces and action of the oscillator algebra.
• Noncommutative symmetric functions
• Uhlenbeck spaces for \(\mathbb{A}^2\) and affine Lie algebra \(\widehat {\mathfrak {sl}}_n\)
• Gelfand–Tsetlin Bases for Classical Lie Algebras
• Global Intersection Cohomology of Quasimaps' Spaces
• Three Combinatorial Models for $$ _ $$ Crystals, with Applications to Cylindric Plane Partitions
• Skew Schur functions and Yangian actions on irreducible integrable modules of \(\widehat{{\mathfrak{gl}}_N}\)
• Quiver varieties and Yangians