Let $R$ be a commutative ring. The purpose of this article is to introduce a new class of ideals of R called weakly irreducible ideals. This class could be a generalization of the families quasi-primary ideals and strongly irreducible ideals. The relationships between the notions primary, quasi-primary, weakly irreducible, strongly irreducible and irreducible ideals, in different rings, has bee...

Character measure is a probability on irreducible representations of semisimple Lie algebra. It appears from the decomposition into irreducibles tensor power fundamental representation. In this paper we calculate asymptotics character so2n+1 in regime near boundary weight diagram. We find out that it converges to Poisson-type distribution.

Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the gr...

Brauer's centralizer algebras are finite dimensional algebras with a distinguished basis. Each Brauer centralizer algebra contains the group algebra of a symmetric group as a subalgebra and the distinguished basis of the Brauer algebra contains the permutations as a subset. In view of this containment it is desirable to generalize as many known facts concerning the group algebra of the symmetri...

We study the representation theory of the W-algebra Wk(ḡ) associated with a simple Lie algebra ḡ at level k. We show that the “−” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any level k ∈ C. Moreover, we show that the character of each irreducible highest weight representation of Wk(ḡ) is completely determined by that of the corresponding irred...

Let L = H(2r; n) be a graded Lie algebra of Hamiltonian type in the Cartan type series over an algebraically closed field of characteristic p > 2. In the generalized restricted Lie algebra setup, any irreducible representation of L corresponds uniquely to a (generalized) p-character χ. When the height of χ is no more than min{pni − pni−1 | i = 1, 2, . . . , 2r} − 2, the corresponding irreducibl...

An example of a strong invariant of an admissible representation (by which I mean an invariant capable of splitting points in Ĝadm) is the distributional character of a representation. Let G be a reductive Lie group, (π,H) an irreducible admissible representation of G and HK is associated Harish-Chandra (g,K)-module, and let Θπ be its distributional character Θπ (f) ≡ TrH (∫ f (g)π (g) dg ) , ∀...

The irreducible representations of the double cover of SL(m) with infinitesmal character 1p having a maximal primitive ideal are determined. We investigate whether these representations are attached to a nilpotent orbit and use the orbit method to speculate their K types. We conclude with a character formula expressing the representations as a sum of simpler virtual representions. Thesis Superv...

Weyl’s character formula is a useful tool in understanding the structure of irreducible representations of semisimple Lie algebras. Even more important than the character formula itself is a corollary, the Weyl dimension formula, which gives a fairly simple expression for the total dimension of the representation in terms of the root system of the Lie algebra. Although the results discussed are...

Given natural numbers m and n, we define a deflation map from the characters of the symmetric group Smn to the characters of Sn. This map is defined by first restricting a character of Smn to the wreath product Sm oSn, and then taking the sum of the irreducible constituents of the restricted character on which the base group Sm × · · · × Sm acts trivially. We prove a combinatorial formula which...