We study a class of representations called “calibrated representations” of the degenerate double affine Hecke algebra and those of the rational Cherednik algebra of type GLn. We give a realization of calibrated irreducible modules as spaces of coinvariants constructed from integrable modules over the affine Lie algebra ĝl m . Moreover, we give a character formula of these irreducible modules in...

We continue our study of the representation theory of a finite dimensional semisimple Lie algebra g by introducing and studying the category O of g-modules that has appeared in the seminal paper by Bernstein, Israel and Sergei Gelfand, [BGG]. We establish a block decomposition for this category and use this to prove the Weyl character formula for finite dimensional irreducible g-modules. Then w...

A theory of highest weight modules over an arbitrary nite-dimensional Lie su-peralgebra is constructed. A necessary and suucient condition for the nite-dimensionality of such modules is proved. Generic nite-dimensional irreducible representations are deened and an explicit character formula for such representations is written down. It is conjectured that this formula applies to any generic nite...

An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with unit row sums. We show how the adoption of ...

A result of Roquette 3] states that if D is an absolutely irreducible representation of a p-group G over the eld of complex numbers, then D can be realized in K((g) j g 2 G), where is the character of D and K = Q or K = Q(i) according to whether p 6 = 2 or p = 2. Based on Baum and Clausen's 1] algorithm for computing the irreducible representations of supersolvable groups, we give an elementary...

We define exact functors from categories of Harish-Chandra modules for certain real classical groups to finite-dimensional modules over an associated graded affine Hecke algebra with parameters. We then study some of the basic properties of these functors. In particular, we show that they map irreducible spherical representations to irreducible spherical representations and, moreover, that they...

It is shown how to associate to a highest weight Λ of the Lie superalgebra gl(m|n) a composite partition ν; μ with composite Young diagram F (ν; μ). The corresponding supersymmetric Schur function sν;μ(x/y) is defined. However, it is known that this S-function does not always coincide with the character of the irreducible representation VΛ with highest weight Λ. Only for covariant, contravarian...

We generalize Regev's results on a virtual character of the symmetric group [Formula: see text], that is, an integer-combination some irreducible characters. Suppose text] and are integer partitions text]. For associated when we find another partition related to such by character. Applying this result, obtain class nonzero Kronecker coefficients Pak et al.'s criterion. Moreover, discuss effecti...