Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · math/0311472

On orbital variety closures in sl(n). I. Induced Duflo order

Anna Melnikov
View original source ↗Read source document ↗Export metadata ↓

Abstract

For a semisimple Lie algebra g the orbit method attempts to assign representations of g to (coadjoint) orbits in g*. Orbital varieties are particular Lagrangian subvarieties of such orbits leading to highest weight representations of g. In sl(n) orbital varieties are described by Young tableaux. Inclusion relation on orbital variety closures defines a partial order on Young tableaux. Our aim is to describe this order. The paper is devoted to the combinatorial description of induced Duflo order on Young tableaux (the order generated by inclusion of generating subspaces of orbital varieties). This is a very interesting and complex combinatorial question. This is the first paper in the series. In Part II and Part III we use repeatedly the results of the paper as a basis for further study of orbital variety closures.

Explore related subjects

math.RTmath.CO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Anna Melnikov. 2003-11-26. On orbital variety closures in sl(n). I. Induced Duflo order. https://arxiv.org/abs/math/0311472

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

On singular supports of Lusztig's perverse sheaves

We prove a conjecture of Lusztig on a microlocal characterization of his perverse sheaves. For any finite quiver without loops, an equivariant simple perverse sheaf on the variety of quiver representations is a Lusztig's perverse sheaf if and only if its singular support is contained in Lusztig's Lagrangian variety, that is, the variety of nilpotent representations of the preprojective algebra of the quiver.

math.RT↗
arXiv2026

Skein algebras and quantized Coulomb branches

To a compact oriented surface of genus at most one with boundary, we associate a quantized $K$-theoretic Coulomb branch in the sense of Braverman, Finkelberg, and Nakajima. In the case where the surface is a three- or four-holed sphere or a one-holed torus, we describe a relationship between this quantized Coulomb branch and the Kauffman bracket skein algebra of the surface. We formulate a general conjecture relating these algebras.

math.RT↗
arXiv2026

Quiver presentations for band algebras are defined over the integers

A band is a semigroup in which each element is idempotent. In recent years, there has been a lot of activity on the representation theory of the subclass of left regular bands due to connections to Markov chains associated to hyperplane arrangements, oriented matroids, matroids and CAT(0) cube complexes. We prove here that the integral semigroup algebra of a band is isomorphic to the integral path algebra of a quiver modulo an admissible ideal. This leads to a uniform bound quiver presentation for band algebras over all fields. Also, we answer a question of Margolis, Saliola and Steinberg by proving that the integral semigroup algebra of a CW left regular band is isomorphic to the quotient of the integral path algebra of the Hasse diagram of its support semilattice modulo the ideal generated by the sum of all paths of length two. This includes, for example, hyperplane face semigroup algebras.

math.RT↗