Extremal cocycles of Weyl groups

DOI10.1007/BF02577133zbMath0633.17008MaRDI QIDQ1096001

D. P. Zhelobenko

Publication date: 1987

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

zbMATH Keywords

Verma modulesenveloping algebraroot systemreductive Lie algebrascomplex Lie algebraextremal equationsextremal projections

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Simple, semisimple, reductive (super)algebras (17B20)

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Mickelsson algebras and representations of Yangians, Constructive modules and extremal projectors over Chevalley algebras, Factorizations of relative extremal projectors, Fermionic formulas for eigenfunctions of the difference Toda Hamiltonian, Auslander-Reiten quiver of type D and generalized quantum affine Schur-Weyl duality, Auslander-Reiten quiver and representation theories related to KLR-type Schur-Weyl duality, Reduced decompositions in Weyl groups, Combinatorial Auslander-Reiten quivers and reduced expressions, Representations of quantum groups at roots of unity, Whittaker vectors and \(q\)-\(W\) algebras, Extremal projectors in the semi-classical case, The geometric meaning of Zhelobenko operators, The structure of q-W algebras, Differential calculus on \(\mathbf{h}\)-deformed spaces, Analogue Zhelobenko invariants, Bernstein-Gelfand-Gelfand operators and the Kostant Clifford algebra conjecture, A generalized Harish-Chandra isomorphism, A categorical approach to dynamical quantum groups, Mickelsson algebras and Zhelobenko operators., Rational representations of the Yangian \(\text Y(\mathfrak {gl}_n)\), Conjugacy classes in Weyl groups and q-W algebras, Reflection equation and twisted Yangians, Small quantum groups associated to Belavin-Drinfeld triples, Tetrahedron and 3D reflection equation from PBW bases of the nilpotent subalgebra of quantum superalgebras, Twisted Yangians and Mickelsson Algebras. II, Twisted and folded Auslander-Reiten quivers and applications to the representation theory of quantum affine algebras, Universal Verma modules and \(W\)-resolvents over Kac-Moody algebras, Hypergeometric solutions of trigonometric KZ equations satisfy dynamical difference equations

Cites Work

• Factorizing particles on a half-line and root systems
• Extremal-type equations and their resolvents over reductive Lie algebras
• Step algebras of semi-simple subalgebras of Lie algebras
• On the Demazure character formula
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