Namespaces
Variants
Actions

Kirillov conjecture

From Encyclopedia of Mathematics
Revision as of 17:07, 7 February 2011 by 127.0.0.1 (talk) (Importing text file)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Let be a local field and an irreducible unitary representation of . Let

Then is irreducible (cf. also Irreducible representation).

A related conjecture is that for two irreducible representations and of, respectively, and , the product

is irreducible.

For non-Archimedean (cf. also Archimedean axiom), both conjectures are true (Bernstein's theorems).

For , these conjectures have been proved by S. Sahi [a1].

References

[a1] S. Sahi, "On Kirillov's conjecture for Archimedean fields" Compositio Math. , 72 : 1 (1989) pp. 67–86
How to Cite This Entry:
Kirillov conjecture. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Kirillov_conjecture&oldid=42875
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article