The BRST reduction of the chiral Hecke algebra
نویسنده
چکیده
We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a ĝκ-module that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its untwisted BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds between the regular cohomology and the Iwahori orbits on the affine flag manifold. As an application of the above, we describe the BRST reduction of the chiral Hecke algebra as a vertex super algebra. 2000 Mathematics Subject classification: 17B99.
منابع مشابه
BRST Reduction of the chiral Hecke Algebra
We explore the relationship between de Rham and Lie algebra cohomologies in the finite dimensional and affine settings. In particular, given a ĝκmodule that arises as the global sections of a twisted D-module on the affine flag manifold, we show how to compute its BRST reduction modulo n(K) using the de Rham cohomology of the restrictions to N(K) orbits. A similar relationship holds between the...
متن کاملOn the irreducibility of the complex specialization of the representation of the Hecke algebra of the complex reflection group $G_7$
We consider a 2-dimensional representation of the Hecke algebra $H(G_7, u)$, where $G_7$ is the complex reflection group and $u$ is the set of indeterminates $u = (x_1,x_2,y_1,y_2,y_3,z_1,z_2,z_3)$. After specializing the indetrminates to non zero complex numbers, we then determine a necessary and sufficient condition that guarantees the irreducibility of the complex specialization of the repre...
متن کاملAlgebraic and Geometric Structures in String Backgrounds
We give a brief introduction to the study of the algebraic structures – and their geometrical interpretations – which arise in the BRST construction of a conformal string background. Starting from the chiral algebra A of a string background, we consider a number of elementary but universal operations on the chiral algebra. From these operations we deduce a certain fundamental odd Poisson struct...
متن کامل/ 95 04 05 1 v 1 1 1 A pr 1 99 5 Chiral and axial anomalies in the framework of generalized
The regularization scheme is proposed for the constrained Hamil-tonian formulation of the gauge fields coupled to the chiral or axial fermions. The Schwinger terms in the regularized operator first-class constraint algebra are shown to be consistent with the covariant divergence anomaly of the corresponding current. Regularized quantum master equations are studied, and the Schwinger terms are f...
متن کاملArithmetic Teichmuller Theory
By Grothedieck's Anabelian conjectures, Galois representations landing in outer automorphism group of the algebraic fundamental group which are associated to hyperbolic smooth curves defined over number fields encode all arithmetic information of these curves. The goal of this paper is to develope and arithmetic teichmuller theory, by which we mean, introducing arithmetic objects summarizing th...
متن کامل