Symmetric representations of holomorphic functions

Holomorphic extensions of representations : ( I ) automorphic functions

Let G be a connected, real, semisimple Lie group contained in its complexification GC, and let K be a maximal compact subgroup of G. We construct a KC-G double coset domain in GC, and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficien...

Bounded Holomorphic Functions on Bounded Symmetric Domains

Let D be a bounded homogeneous domain in C , and let A denote the open unit disk. If z e D and /: D —► A is holomorphic, then ß/(z) is defined as the maximum ratio \Vz(f)x\/Hz(x, 3c)1/2 , where x is a nonzero vector in C and Hz is the Bergman metric on D . The number ßf(z) represents the maximum dilation of / at z . The set consisting of all ß/(z), for z e D and /: D —► A holomorphic, is known ...

Alcove walks, buildings, symmetric functions and representations

For a complex simple Lie algebra g, the dimension Kλμ of the μ weight space of a finite dimensional representation of highest weight λ is the same as the number of Littelmann paths of type λ and weight μ. In this paper we give an explicit construction of a path of type λ and weight μ whenever Kλμ 6= 0. This construction has additional consequences, it produces an explicit point in the building ...

Hopf Algebras, Symmetric Functions and Representations

1.1. Motivation. Much of representation theory can be unified by considering the representation theory of associative algebras. Specifically, the representation theory of Lie algebras may be studied via the representations of universal enveloping algebras; the representation theory of finite groups studied via the representation theory of the group algebra; the representation theory of quivers ...

The symmetric group - representations, combinatorial algorithms, and symmetric functions