2,931 research outputs found
Homogeneous components in the moduli space of sheaves and Virasoro characters
The moduli space of framed torsion free sheaves on the
projective plane with rank and second Chern class equal to has the
natural action of the -dimensional torus. In this paper, we look at the
fixed point set of different one-dimensional subtori in this torus. We prove
that in the homogeneous case the generating series of the numbers of the
irreducible components has a beautiful decomposition into an infinite product.
In the case of odd these infinite products coincide with certain Virasoro
characters. We also propose a conjecture in a general quasihomogeneous case.Comment: Published version, 19 page
Quasiinvariants of Coxeter groups and m-harmonic polynomials
The space of m-harmonic polynomials related to a Coxeter group G and a
multiplicity function m on its root system is defined as the joint kernel of
the properly gauged invariant integrals of the corresponding generalised
quantum Calogero-Moser problem. The relation between this space and the ring of
all quantum integrals of this system (which is isomorphic to the ring of
corresponding quasiinvariants) is investigated.Comment: 23 page
Ramanujan's "Lost Notebook" and the Virasoro Algebra
By using the theory of vertex operator algebras, we gave a new proof of the
famous Ramanujan's modulus 5 modular equation from his "Lost Notebook" (p.139
in \cite{R}). Furthermore, we obtained an infinite list of -identities for
all odd moduli; thus, we generalized the result of Ramanujan.Comment: To appear in Comm. Math. Phy
Functional realization of some elliptic Hamiltonian structures and bosonization of the corresponding quantum algebras
We introduce a functional realization of the Hamiltonian structure on the
moduli space of P-bundles on the elliptic curve E. Here P is parabolic subgroup
in SL_n. We also introduce a construction of the corresponding quantum
algebras.Comment: 20 pages, Amstex, minor change
Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations
We study the conformal vertex algebras which naturally arise in relation to
the Nakajima-Yoshioka blow-up equations.Comment: 23 pages v2. 24 pages, references added, proofs in section 3 are
expanded, many typos correcte
On algebraic equations satisfied by hypergeometric correlators in WZW models. II
We give an explicit description of "bundles of conformal blocks" in
Wess-Zumino-Witten models of Conformal field theory and prove that integral
representations of Knizhnik-Zamolodchikov equations constructed earlier by the
second and third authors are in fact sections of these bundles.Comment: 32 pp., amslate
Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation
We represent a classical Maxwell-Bloch equation and related to it positive
part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is
given by an infinitesimal action of a nilpotent subalgebra of affine Lie
algebra on a Maxwell-Bloch phase space treated as a homogeneous
space of . A space of local integrals of motion is described using
cohomology methods. We show that hamiltonian flows associated to the
Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are
identified with an infinitesimal action of an abelian subalgebra of the
nilpotent subalgebra on a Maxwell- Bloch phase space. Possibilities of
quantization and latticization of Maxwell-Bloch equation are discussed.Comment: 16 pages, no figures, plain TeX, no macro
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