(GLn+1(F), GLn(F)) is a Gelfand pair for any local field F

A Gelfand Pair for Any Local Field

Let F be an arbitrary local field. Consider the standard embedding GLn(F ) →֒ GLn+1(F ) and the two-sided action of GLn(F )×GLn(F ) on GLn+1(F ). In this paper we show that any GLn(F ) × GLn(F )-invariant distribution on GLn+1(F ) is invariant with respect to transposition. We show that this implies that the pair (GLn+1(F ), GLn(F )) is a Gelfand pair. Namely, for any irreducible admissible repr...

A Gelfand Pair for Any Quadratic Space V over a Local Field

Let V be a quadratic space with a form q over an arbitrary local field F of characteristic different from 2. Let W = V ⊕ Fe with the form Q extending q with Q(e) = 1. Consider the standard embedding O(V ) ↪→ O(W ) and the two-sided action of O(V )×O(V ) on O(W ). In this note we show that any O(V )×O(V )-invariant distribution on O(W ) is invariant with respect to transposition. This result was...

Any Pair of 2D Curves Is Consistent with a 3D

Symmetry has been shown to be a very effective a priori constraint in solving a 3D shape recovery problem. Symmetry is useful in 3D recovery because it is a form of redundancy. There are, however, some fundamental limits to the effectiveness of symmetry. Specifically, given two arbitrary curves in a single 2D image, one can always find a 3D mirror-symmetric interpretation of these curves under ...

Cofiniteness of Local Cohomlogy Based on a Non–Closed Support Defined by a Pair of Ideals

On the f-vectors of Gelfand-Cetlin polytopes

A Gelfand-Cetlin polytope is a convex polytope obtained as an image of certain completely integrable system on a partial flag variety. In this paper, we give an equivalent description of the face structure of a GC-polytope in terms of so called the face structure of a ladder diagram. Using our description, we obtain a partial differential equation whose solution is the exponential generating fu...