相关论文: Stable branching rules for classical symmetric pai…

We find the branching laws for the classical pairs $\mathrm{GL}(m, \mathbb{C}) \subset \mathrm{GL}(n, \mathbb{C})$, $\mathrm{Sp}(2m, \mathbb{C}) \subset \mathrm{Sp}(2n, \mathbb{C})$, $\mathrm{SO}(q, \mathbb{C}) \subset \mathrm{SO}(p,…

We give a new formula for the branching rule from ${\rm GL}_n$ to ${\rm O}_n$ generalizing the Littlewood's restriction formula. The formula is given in terms of Littlewood-Richardson tableaux with certain flag conditions which vanish in a…

We study branching laws for a classical group $G$ and a symmetric subgroup $H$. Our approach is through the {\it branching algebra}, the algebra of covariants for $H$ in the regular functions on the natural torus bundle over the flag…

The classical Littlewood-Richardson coefficients C(lambda,mu,nu) carry a natural $S_3$ symmetry via permutation of the indices. Our "carton rule" for computing these numbers transparently and uniformly explains these six symmetries;…

We study algebras encoding stable range branching rules for the pairs of complex classical groups of the same type in the context of toric degenerations of spherical varieties. By lifting affine semigroup algebras constructed from…

Starting from a recently found branching formula for the six-parameter family of symmetric Macdonald-Koornwinder polynomials, we arrive by degeneration at corresponding branching rules for symmetric hypergeometric orthogonal polynomials of…

We construct a natural branch divisor for equidimensional projective morphisms where the domain has lci singularities and the target is nonsingular. The method involves generalizing a divisor contruction of Mumford from sheaves to…

Littlewood-Richardson rule gives the decomposition formula for the multiplication of two Schur functions, while the decomposition formula for the multiplication of two Hall-Littlewood functions or two universal characters is also given by…

For a given skew shape, we build a crystal graph on the set of all reverse plane partitions that have this shape. As a consequence, we get a simple extension of the Littlewood-Richardson rule for the expansion of the corresponding dual…

We introduce a family of rings of symmetric functions depending on an infinite sequence of parameters. A distinguished basis of such a ring is comprised by analogues of the Schur functions. The corresponding structure coefficients are…

A fundamental problem in the representation theory of the symmetric group, Sn, is to describe the coefficients in the decomposition of a tensor product of two simple representations. These coefficients are known in the literature as the…

We produce a family of reductions for Schubert intersection problems whose applicability is checked by calculating a linear combination of the dimensions involved. These reductions do not alter the Littlewood-Richardson coefficient, and…

We study the classical, two-sided stable marriage problem under pairwise preferences. In the most general setting, agents are allowed to express their preferences as comparisons of any two of their edges and they also have the right to…

We describe an explicit geometric Littlewood-Richardson rule, interpreted as deforming the intersection of two Schubert varieties so that they break into Schubert varieties. There are no restrictions on the base field, and all…

We systematically derive the Lax pair formulation for both discrete and continuum integrable classical theories with consistent boundary conditions.

We propose a generalization of the classical stable marriage problem. In our model, the preferences on one side of the partition are given in terms of arbitrary binary relations, which need not be transitive nor acyclic. This generalization…

DNS and laboratory experiments show that the spatial distribution of straining stagnation points in homogeneous isotropic 3D turbulence has a fractal structure with dimension D_s = 2. In Kinematic Simulations the time exponent gamma in…

We study natural quantizations of branching coefficients corresponding to the restrictions of the classical Lie groups to their Levi subgroups. We show that they admit a stable limit which can be regarded as a $q$-analogue of a tensor…

By using a generalization of Sturm-Liouville problems in discrete spaces, a basic class of symmetric orthogonal polynomials of a discrete variable with four free parameters, which generalizes all classical discrete symmetric orthogonal…

The stable marriage problem is a well-known problem of matching men to women so that no man and woman, who are not married to each other, both prefer each other. Such a problem has a wide variety of practical applications, ranging from…