Let X be a Banach space, H a subspace of X, M an n-dimensional subspace of H and D a linear operator from H to X. R. Whitley raised the question how to calculate the following numbers:
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
基金Project supported by the Science Fund of Academia Sinica.
文摘Let X be a Banach space, H a subspace of X, M an n-dimensional subspace of H and D a linear operator from H to X. R. Whitley raised the question how to calculate the following numbers:
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.
