507 research outputs found
Standard Monomial Theory for Bott-Samelson Varieties of GL(n)
We construct an explicit basis for the coordinate ring of the Bott-Samelson
variety Z_i associated to G = GL(n) and an arbitrary sequence of simple
reflections i. Our basis is parametrized by certain standard tableaux and
generalizes the Standard Monomial basis for Schubert varieties. Our standard
tableaux have a natural crystal graph structure.Comment: Northeastern University, [email protected] AMSTeX amspp
New and Old Results in Resultant Theory
Resultants are getting increasingly important in modern theoretical physics:
they appear whenever one deals with non-linear (polynomial) equations, with
non-quadratic forms or with non-Gaussian integrals. Being a subject of more
than three-hundred-year research, resultants are of course rather well studied:
a lot of explicit formulas, beautiful properties and intriguing relationships
are known in this field. We present a brief overview of these results,
including both recent and already classical. Emphasis is made on explicit
formulas for resultants, which could be practically useful in a future physics
research.Comment: 50 pages, 15 figure
Unitary One Matrix Models: String Equations and Flows
We review the Symmetric Unitary One Matrix Models. In particular we discuss
the string equation in the operator formalism, the mKdV flows and the Virasoro
Constraints. We focus on the \t-function formalism for the flows and we
describe its connection to the (big cell of the) Sato Grassmannian \Gr via
the Plucker embedding of \Gr into a fermionic Fock space. Then the space of
solutions to the string equation is an explicitly computable subspace of
\Gr\times\Gr which is invariant under the flows.Comment: 20 pages (Invited talk delivered by M. J. Bowick at the Vth Regional
Conference on Mathematical Physics, Edirne Turkey: December 15-22, 1991.
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