ユニタリ表現論セミナー報告集X 表紙・目次

ユニタリ表現論セミナー報告集 X,

1990

SEMINAR

REPORTS OF

UNITARY REPRESENTATION

Seminar Reports of Unitary Representation No. 10

-contents-S. Aoki and S. Kato: Connection formula for invariant

eigendistributions

on

$U$

$(p , q)/\{ U(r)\cross U (p- r , q)\}$

. .

. .

.

1

A. Bak: Nonaberian $K$-theory and the $K$-theory of Kac-Moody groups

. .

.

6

A. S. Dzhumadil’ _{daev: Nonsplit extensions of Lie algebras and their}

irreducible representations

. .

.

.

.

7

H. Fujiwara: Plancherel formula for monomial representations of

nilpotent Lie groups

. . . .

.

8

A. Guichardet: On

some

categaries of $( \mathfrak{g} , K)$ -modules

.

.

.

.

10

K. Hasegawa and Y. Yamada: Algebraic derivation of ”Broken

$Z_{N}$-symmetric” solutions for the star-triangle relations

.

. .

.

13

A.G. Helminck: Some results

on

symmetric varieties

. .

.

.

18

G. F. Helminck: Projective holomorphic representations of the

restricted linear group

. . .

.

19

J.S. Huang: $K$-$bi$-finite and $Z(\mathfrak{g})$-finite functions

. .

.

.

24

E. Kaniuth: The Pompeiu problem for groups

.

.

.

.

29

K. Kariyama: Note

on

Weyl-Harish-Chandra character formula for tamely ramified supercupidal representations of $GL_{n}$

.

. .

.

32

T. Kawazoe: A method of reduction

to

the spherical

case

in

harmonic analysis

on

real rank 1 semisimple Lie groups

.

. .

.

37

T. Kobayashi: Discontinuous group in

a

homogeneous space of reductive

K. Koike: Relative

invariants

of the Polynomial rings

over

the finite

and

tame

type quivers

. . .

_.

₄₆

A. Kowata: Spherical hyperfunctions

_on

_{the tangent space of symmetric}

spaces

_{. . .}

_.

₅₀

R. L. Lipsman: _{The Penney-Fujiwara Plancherel formula for homogeneous}

spaces _{wi th monomial} spectrum

. .

.

_.

₅₃

L. A. _{Mantini: Geometric realizations of unitary highest weight}

modules

as

solutions of

differential

equations

. . .

.

₅₆

B.

rsted:

Spherical

_{distributions}

_on

_{symmetric spaces}

. . .

_.

₆₁

R. Penney: Poisson integrals for homogeneous, _{rank 1 Koszul}

_domains

in $\mathbb{C}^{n}$

. .

.

.

64

S. A.

Salamanca-Riba:

On the unitary representations _of $SO(n , m)$

.

. .

.

₆₉

N. Shimeno: Eigenfunctions _of

_invariant

_differential

_operators

_on

$U(p, q)/U(p-1, q)$

_{. . .}

_.

₇₃

H. Singh: Second order

differential

eqations _{in Lie}

_groups

. .

.

.

₇₆

J. _{Soto-Andrade: Generalized Weil representations for} $SL (n)$

. .

.

.

₈₆

K. Suto: Towards Kac-Moody Lie groups

. .

.

_.

₉₁

I. Terada: A

robinson-Schersted-type

correspondence _for

_a

_dual pair

on

spinors

_{. .}

.

_.

96

S. Yamagami

:

Representations _{of non-semisimple and}

_non-group

_object

.

.

.

.

99

I. _Yokota:

_Realizations

_of

_involutive

_{automorphisms} $\sigma$ and

$G^{\sigma}$

of

exceptional _{linear Lie}

_groups

$G$

.

.

.

101

M. Wakayama: _{The relation between the} $\eta$

-invariant

and the spin