274 research outputs found
Reduction of quantum systems with arbitrary first class constraints and Hecke algebras
We propose a method for reduction of quantum systems with arbitrary first
class constraints. An appropriate mathematical setting for the problem is
homology of associative algebras. For every such an algebra and its
subalgebra B with an augmentation e there exists a cohomological complex which
is a generalization of the BRST one. Its cohomology is an associative graded
algebra Hk^{*}(A,B) which we call the Hecke algebra of the triple (A,B,e). It
acts in the cohomology space H^{*}(B,V) for every left A- module V. In
particular the zeroth graded component Hk^{0}(A,B) acts in the space of B-
invariants of V and provides the reduction of the quantum system.Comment: 15 pages, LaTeX 2
The geometric meaning of Zhelobenko operators
Let g be the complex semisimple Lie algebra associated to a complex
semisimple algebraic group G, b a Borel subalgebra of g, h the Cartan
sublagebra contained in b and N the unipotent subgroup of G corresponding to
the nilradical n of b. We show that the explicit formula for the extremal
projection operator for g obtained by Asherova, Smirnov and Tolstoy and similar
formulas for Zhelobenko operators are related to the existence of a birational
equivalence N\times h -> b given by the restriction of the adjoint action.
Simple geometric proofs of formulas for the "classical" counterparts of the
extremal projection operator and of Zhelobenko operators are also obtained.Comment: 9 pages, final versio
An analogue of the operator curl for nonabelian gauge groups and scattering theory
We introduce a new perturbation for the operator curl related to connections
with nonabelian gauge groups. We also prove that the perturbed operator is
unitary equivalent to the operator curl if the corresponding connection is
close enough to the trivial one with respect to a certain topology on the space
of connections.Comment: 14 page
Strictly transversal slices to conjugacy classes in algebraic groups
We show that for every conjugacy class O in a connected semisimple algebraic
group G over a field of characteristic good for G one can find a special
transversal slice S to the set of conjugacy classes in G such that O intersects
S and dim O = codim S.Comment: 38 pages; minor modification
Semi-infinite cohomology and Hecke algebras
This paper provides a homological algebraic foundation for generalizations of
classical Hecke algebras introduced in math.QA/9805134. These new Hecke
algebras are associated to triples of the form (A,B,e), where A is an
associative algebra containing subalgebra B with character e.
These algebras are connected with cohomology of associative algebras in the
sense that for every left A-module V and right A-module W the Hecke algebra
associated to triple (A,B,e) naturally acts in the B-cohomology and B-homology
spaces of V and W, respectively.
We also introduce the semi-infinite cohomology functor for associative
algebras and define modifications of Hecke algebras acting in semi-infinite
cohomology spaces. We call these algebras semi-infinite Hecke algebras.
As an example we realize the W-algebra W(g) associated to a complex
semisimple Lie algebra g as a semi-infinite Hecke algebra. Using this
realization we explicitly calculate the algebra W(g) avoiding the bosonization
technique used by Feigin and Frenkel.Comment: 45 pages, AMSLaTeX, 1 figure using XY-pi
The classical r-matrix method for nonlinear sigma-model
The canonical Poisson structure of nonlinear sigma-model is presented as a
Lie-Poisson r-matrix bracket on coadjoint orbits. It is shown that the Poisson
structure of this model is determined by some `hidden singularities' of the Lax
matrix.Comment: 18 pages, LaTe
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