96 research outputs found
A BGG-type resolution for tensor modules over general linear superalgebra
We construct a Bernstein-Gelfand-Gelfand type resolution in terms of direct
sums of Kac modules for the finite-dimensional irreducible tensor
representations of the general linear superalgebra. As a consequence it follows
that the unique maximal submodule of a corresponding reducible Kac module is
generated by its proper singular vector.Comment: 11pages, LaTeX forma
Schur Q-functions and degeneracy locus formulas for morphisms with symmetries
We give closed-form formulas for the fundamental classes of degeneracy loci
associated with vector bundle maps given locally by (not necessary square)
matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal.
Our description uses essentially Schur Q-polynomials of a bundle, and is based
on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear
in the Proceedings of Intersection Theory Conference in Bologna, "Progress in
Mathematics", Birkhause
Crystal Graphs and -Analogues of Weight Multiplicities for the Root System
We give an expression of the -analogues of the multiplicities of weights
in irreducible \sl_{n+1}-modules in terms of the geometry of the crystal
graph attached to the corresponding U_q(\sl_{n+1})-modules. As an
application, we describe multivariate polynomial analogues of the
multiplicities of the zero weight, refining Kostant's generalized exponents.Comment: LaTeX file with epic, eepic pictures, 17 pages, November 1994, to
appear in Lett. Math. Phy
Irreducible Characters of General Linear Superalgebra and Super Duality
We develop a new method to solve the irreducible character problem for a wide
class of modules over the general linear superalgebra, including all the
finite-dimensional modules, by directly relating the problem to the classical
Kazhdan-Lusztig theory. We further verify a parabolic version of a conjecture
of Brundan on the irreducible characters in the BGG category \mc{O} of the
general linear superalgebra. We also prove the super duality conjecture
Vicious Walkers and Hook Young Tableaux
We consider a generalization of the vicious walker model. Using a bijection
map between the path configuration of the non-intersecting random walkers and
the hook Young diagram, we compute the probability concerning the number of
walker's movements. Applying the saddle point method, we reveal that the
scaling limit gives the Tracy--Widom distribution, which is same with the limit
distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure
Crystal energy functions via the charge in types A and C
The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic
which we call charge. In types A and C it can be defined on tensor products of
Kashiwara-Nakashima single column crystals. In this paper we prove that the
charge is equal to the (negative of the) energy function on affine crystals.
The algorithm for computing charge is much simpler and can be more efficiently
computed than the recursive definition of energy in terms of the combinatorial
R-matrix.Comment: 25 pages; 1 figur
Super duality and irreducible characters of ortho-symplectic Lie superalgebras
We formulate and establish a super duality which connects parabolic
categories between the ortho-symplectic Lie superalgebras and classical Lie
algebras of types. This provides a complete and conceptual solution of
the irreducible character problem for the ortho-symplectic Lie superalgebras in
a parabolic category , which includes all finite-dimensional irreducible
modules, in terms of classical Kazhdan-Lusztig polynomials.Comment: 30 pages, Section 5 rewritten and shortene
A New Young Diagrammatic Method For Kronecker Products of O(n) and Sp(2m)
A new simple Young diagrammatic method for Kronecker products of O(n) and
Sp(2m) is proposed based on representation theory of Brauer algebras. A general
procedure for the decomposition of tensor products of representations for O(n)
and Sp(2m) is outlined, which is similar to that for U(n) known as the
Littlewood rules together with trace contractions from a Brauer algebra and
some modification rules given by King.Comment: Latex, 11 pages, no figure
Supersymmetric holography on AdS3
The proposed duality between Vasiliev's supersymmetric higher spin theory on
AdS3 and the 't Hooft limit of the 2d superconformal Kazama-Suzuki models is
analysed in detail. In particular, we show that the partition functions of the
two theories agree in the large N limit.Comment: 25 pages, 3 figures, improved fig.
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