7,168 research outputs found
PBW filtration and bases for symplectic Lie algebras
We study the PBW filtration on the highest weight representations V(\la) of
\msp_{2n}. This filtration is induced by the standard degree filtration on
U(\n^-). We give a description of the associated graded S(\n^-)-module gr
V(\la) in terms of generators and relations. We also construct a basis of gr
V(\la). As an application we derive a graded combinatorial formula for the
character of V(\la) and obtain a new class of bases of the modules V(\la).Comment: 21 page
Embedding of bases: from the M(2,2k+1) to the M(3,4k+2-delta) models
A new quasi-particle basis of states is presented for all the irreducible
modules of the M(3,p) models. It is formulated in terms of a combination of
Virasoro modes and the modes of the field phi_{2,1}. This leads to a fermionic
expression for particular combinations of irreducible M(3,p) characters, which
turns out to be identical with the previously known formula. Quite remarkably,
this new quasi-particle basis embodies a sort of embedding, at the level of
bases, of the minimal models M(2,2k+1) into the M(3,4k+2-delta) ones, with 0
\leq delta \leq 3.Comment: corrected a typo in the title, 7 page
Schubert varieties and the fusion products
For each we define a Schubert variety as a closure of the
\Slt(\C[t])-orbit in the projectivization of the fusion product . We
clarify the connection of the geometry of the Schubert varieties with an
algebraic structure of as \slt\otimes\C[t] modules. In the case when
all the entries of are different is smooth projective algebraic
variety. We study its geometric properties: the Lie algebra of the vector
fields, the coordinate ring, the cohomologies of the line bundles. We also
prove, that the fusion products can be realized as the dual spaces of the
sections of these bundles.Comment: 34 page
Two dimensional current algebras and affine fusion product
In this paper we study a family of commutative algebras generated by two
infinite sets of generators. These algebras are parametrized by Young diagrams.
We explain a connection of these algebras with the fusion product of integrable
irreducible representations of the affine Lie algebra. As an application
we derive a fermionic formula for the character of the affine fusion product of
two modules. These fusion products can be considered as a simplest example of
the double affine Demazure modules.Comment: 22 page
Quasi-invariants of dihedral systems
A basis of quasi-invariant module over invariants is explicitly constructed
for the two-dimensional Coxeter systems with arbitrary multiplicities. It is
proved that this basis consists of -harmonic polynomials, thus the earlier
results of Veselov and the author for the case of constant multiplicity are
generalized.Comment: 22 pages; a minor correction done; accepted by Mathematical Note
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