Access the full text.
Sign up today, get DeepDyve free for 14 days.
Let G be a connected, simply connected nilpotent Lie group and ΓΓ a lattice subgroup of G . The quasi regular representation decomposes as a direct sum of unitary irreducible representations of G . The nilmanifold G /ΓΓ is called nilmanifold with flat orbits if the coadjoint orbit corresponding to any element of the spectrum of ℛ ΓΓ is flat. In this note, we give a new multiplicity formula related to the decomposition into irreducibles of ℛ ΓΓ in the case when G /ΓΓ is a nilmanifold with flat orbits. As an application, we first prove that every nilmanifold with flat orbits satisfies the Moore formula. We also give partial answers to some related questions proposed by Brezin and by Corwin and Greenleaf.
Advances in Pure and Applied Mathematics – de Gruyter
Published: Sep 1, 2011
Keywords: Nilpotent Lie group; lattice subgroup; rational structure; unitary representation; co-adjoint orbit; Kirillov theory
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.