Boundeness of a Class of Maximal Operators on H^p Spaces on Compact Lie Groups

In this paper we discuss the weak type(IP,I)boundedness of a class of maximal operators T and themaximal strong,mean boundedness of a family of the operators {T on the atomic IP spaces on compaet Lie groups.Also,we obtain the correspoding convergent rosults.

The Hypoellipticity for a Class of Nonhomogeneous Convolution Operator on the Nilpotent Lie Group H^n×R^k

In this paper,we use the method of representation of Lie group to study a class of nonhomoge- neous convolution operator on the nilpotent Lie group H^M×R^k,and give a criteerion of their hypoellipticity.

A NEW TYPE OF PRONORMAT SUBGROUPS IN CHEVALLEY GROUPS

Let L be a simple Lie algebra with irreducible root system. having roots of different length, F be a field of charaCteristic different from 2, G = L(F) be a Chevalley group of type L over F. Denote by Φl the set of all long roots in Φl Set Gl = <xr (t); f∈EΦl,t∈F>. It is a subgroup of G generated by all the long root subgroups. This paper determines the pronormality of Gl in G when L is not of type G2.

Dirac cohomology and Dirac induction

Let G be a connected semisimple Lie group with a maximal compact group K of equal rank. We use the Dirac cohomology of the unitary representations to define Dirac-induction from a representation of K to the discrete series of G. This is closely related to the Dirac induction for the reduced group C*-algebras C*red (G) and a geometric construction of discrete series for semisimple Lie groups. Furthermore, we use Dirac cohomology of the Kostant's cubic Dirac operator to define Dirac-induction for compact Lie groups. This induction for compact Lie groups is simpler than the Bott's induction and is easier for calculation.

Grbner-Shirshov Bases of Irreducible Modules of the Quantum Group of Type G_2

First, the authors give a GrSbner-Shirshov basis of the finite-dimensional irre- ducible module Vq（λ） of the Drinfeld-Jimbo quantum group Uq（G2） by using the double free module method and the known GrSbner-Shirshov basis of Uq（G2）. Then, by specializing a suitable version of Uq （G2） at q = 1, they get a GrSbner-Shirshov basis of the universal enveloping algebra U（G2） of the simple Lie algebra of type G2 and the finite-dimensional irreducible U（G2）-module V（λ）.

HORMANDER MULTIPLIER THEOREM ON SU(2)

A boundedness criterion is set up for some convolution operators on a compact Lie group.By this criterion a Hormander multiplier theorem is proved in the Hardy spaces on SU(2).

REPRESENTATIONS OF SOLVABLE LIE GROUPSAND GEOMETRIC QUANTIZATION

Representations of solvable Lie groups are realized and classified by geometric quantization of coadjoint orbits through positive polarizations.

ALGEBRAIC GROUPS ASSOCIATED WITH GRADED LIE ALGEBRAS OF CARTAN TYPE

For a graded simple Lie algebra of Cartan type L=X(m:n) (2) X∈{W,S,H,K} , over a field F of odd characteristic p , the group generated by one-parameter subgroups of the form exp( t ad y )is described, where y∈L+F u satisfying y p=0 , t∈F and u is some fixed element of the p -envelope of L in Der u (m :n).