ON ORBITAL VARIETY CLOSURES IN sln I. INDUCED DUFLO ORDER
نویسنده
چکیده
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 sln 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.
منابع مشابه
ON ORBITAL VARIETY CLOSURES IN sln III.GEOMETRIC PROPERTIES
This is the third paper in the series. Here we define a few combinatorial orders on Young tableaux. The first order is obtained from induced Duflo order by the extension with the help of Vogan Tα,β procedure. We call it Duflo-Vogan order. The second order is obtained from the generalization of Spaltenstein’s construction by consideration of an orbital variety as a double chain of nilpotent orbi...
متن کاملON ORBITAL VARIETY CLOSURES IN sln II. DESCENDANTS OF A RICHARDSON ORBITAL VARIETY
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 sln orbital varieties are described by Young tableaux. In this paper we consider so called Richardson orbital varieties in sln. A Richardson orbital variety ...
متن کاملThe Combinatorics of Orbital Varieties Closures of Nilpotent Order 2 in sln
We consider two partial orders on the set of standard Young tableaux. The first one is induced to this set from the weak right order on symmetric group by Robinson-Schensted algorithm. The second one is induced to it from the dominance order on Young diagrams by considering a Young tableau as a chain of Young diagrams. We prove that these two orders of completely different nature coincide on th...
متن کاملOn the closures of orbits of fourth order matrix pencils
In this work we state a simple criterion for nilpotentness of a square n×n matrix pencil with respect to the action of SLn(C)×SLn(C)×SL2(C). The orbits of matrix pencils are classified explicitly for n = 4 and the hierarchy of closures of nilpotent orbits is described. Also, we prove that the algebra of invariants of the action of SLn(C)× SLn(C)× SL2(C) on C ⊗ C ⊗ C is isomorphic to the algebra...
متن کاملHierarchy of closures of matrix pencils
The focus of this paper is the standard linear representation of the group SLn(C)×SLm(C)×SL2(C), that is, the tensor product of the corresponding tautological representations. Classification of its orbits is a classic problem, which goes back to the works of Kronecker and Weierstrass. Here, we summarize some known results about standard linear representations of SLn(C) × SLm(C) × SL2(C), GLn(C)...
متن کامل