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 s...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.展开更多
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-Shirsh...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）.展开更多
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 descr...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).展开更多
基金supported by research grants from the Research Grant Council of HKSAR, China
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.11061033,11361056)
文摘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）.
文摘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).
