Bounded reductive subalgebras of sl(n)

Details Bounded reductive subalgebras of sl(n) Bounded reductive subalgebras of sl(n)

2010-07-08

arxiv.org/abs/1007.1338v3

Mathematics

Representation Theory

Scientific paper

Let $\mathfrak g$ be a semisimple Lie algebra and $\mathfrak k\subset\mathfrak g$ be a reductive in $\mathfrak g$ subalgebra. A $(\mathfrak g, \mathfrak k)$-module is a $\mathfrak g$-module which after restriction to $\mathfrak k$ becomes a direct sum of finite-dimensional $\mathfrak k$-modules. I.Penkov and V.Serganova introduce definition of bounded $(\mathfrak g, \mathfrak k)$-modules for reductive subalgebras $\mathfrak k\subset\mathfrak g$, i.e. $(\mathfrak g, \mathfrak k)$-modules whose $\mathfrak k$-multiplicities are uniformly bounded. A question arising in this context is, given $\mathfrak g$, to describe all reductive in $\mathfrak g$ bounded subalgebras, i.e. reductive in $\mathfrak g$ subalgebras $\mathfrak k$ for which at least one infinite-dimensional bounded $(\mathfrak g, \mathfrak k)$-module exists. In the present paper we describe explicitly all reductive in $\mathfrak{sl}_n$ bounded subalgebras. Our technique is based on symplectic geometry and the notion of spherical variety. We also characterize the irreducible components of the associated varieties of simple bounded $(\mathfrak g, \mathfrak k)$-modules.

Affiliated with

Also associated with

No associations

Rating

Bounded reductive subalgebras of sl(n) does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Bounded reductive subalgebras of sl(n), we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bounded reductive subalgebras of sl(n) will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-102777