154 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
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
Localization of quantum biequivariant D-modules and q-W algebras
We present a biequivariant version of Kremnizer-Tanisaki localization theorem
for quantum D-modules. We also obtain an equivalence between a category of
finitely generated equivariant modules over a quantum group and a category of
finitely generated modules over a q-W algebra defined in arXiv:1011.2431. This
equivalence can be regarded as an equivariant quantum group version of Skryabin
equivalence. The biequivariant localization theorem for quantum D-modules
together with the equivariant quantum group version of Skryabin equivalence
yield an equivalence between a certain category of quantum biequivariant
D-modules and a category of finitely generated modules over a q-W algebra.Comment: 36 pages; minor corrections. arXiv admin note: text overlap with
arXiv:1011.243
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