27 citations · 72 across the 16 of their papers we have counts for
16 papers
Generating functions of action on symmetric functions
Caleb Fernelius, Natasha Rozhkovskaya
We describe the action of the infinite-dimensional Lie algebra and its B-type analogue on Schur and Schur Q-functions, respectively, using formal distributions frame…
Lattice aggregations of boxes and symmetric functions
Natasha Rozhkovskaya
We introduce two lattice growth models: aggregation of -dimensional boxes and aggregation of partitions with parts. We describe properties of the models: the parameter set o…
On a super-analog of the Schur-Weyl Duality
Alexei Borodin, Natasha Rozhkovskaya
Two super-analogs of the Schur-Weyl duality are considered: the duality of actions in of the Lie superalgebra and the symmetri…
Linear transformations of vertex operator presentations of Hall-Littlewood polynomials
Natasha Rozhkovskaya
We study the effect of linear transformations on quantum fields with applications to vertex operator presentations of symmetric functions. Properties of linearly transformed quantu…
Polynomial Tau-functions of the KP, BKP, and the s-Component KP Hierarchies
Victor G. Kac, Natasha Rozhkovskaya, Johan van de Leur
We show that any polynomial tau-function of the s-component KP and the BKP hierarchies can be interpreted as a zero mode of an appropriate combinatorial generating function. As an…
Boson-fermion correspondence for Hall-Littlewood polynomials revisited
Gabriel Necoechea, Natasha Rozhkovskaya
We connect twisted vertex operator presentation of Hall-Littlewood polynomials with the action of charged free fermions, describe a boson-fermion correspondence that relates twiste…
Multiparameter Schur -Functions Are Solutions of the BKP Hierarchy
Natasha Rozhkovskaya
We prove that multiparameter Schur -functions, which include as specializations factorial Schur -functions and classical Schur -functions, provide solutions of the BKP hie…
Action of Clifford algebra on the space of sequences of transfer operators
Natasha Rozhkovskaya
We deduce from a determinant identity on quantum transfer matrices of generalized quantum integrable spin chain model their generating functions. We construct the isomorphism of Cl…
Generating functions for symmetric and shifted symmetric functions
Naihuan Jing, Natasha Rozhkovskaya
We describe generating functions for several important families of classical symmetric functions and shifted Schur functions. The approach is originated from vertex operator realiz…
Segal-Sugawara vectors for the Lie algebra of type
A. I. Molev, E. Ragoucy, N. Rozhkovskaya
Explicit formulas for Segal-Sugawara vectors associated with the simple Lie algebra of type are found by using computer-assisted calculations. This leads to a…
Vertex operators arising from Jacobi-Trudi identities
Naihuan Jing, Natasha Rozhkovskaya
We give an interpretation of the boson-fermion correspondence as a direct consequence of Jacobi-Trudi identity. This viewpoint enables us to construct from a generalized version of…
A new formula for Pfaffian-type Segal-Sugawara vector
Natasha Rozhkovskaya
A combinatorial formula for Pfaffian for the universal enveloping algebra of the affine Kac - Moody algebra of even orthogonal Lie algebra is proved. It allows easily to compute th…
Characteristic maps for the Brauer algebra
A. I. Molev, N. Rozhkovskaya
The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The…
Sklyanin Determinant for Reflection Algebra
Natasha Rozhkovskaya
Reflection algebras is a class of algebras associated with integrable models with boundaries. The coefficients of Sklyanin determinant generate the center of the reflection algebra…
Symmetric functions for the generating matrix of Yangian of gl_n(C)
Natasha Rozhkovskaya
Analogues of classical combinatorial identities for elementary and homogeneous symmetric functions with coefficients in Yanigian are discussed. As a corollary, similar relations ar…
Braided central elements
Natasha Rozhkovskaya
We present and study two families of polynomials with coefficients in the center of the universal enveloping algebra. These polynomials are analogues of a determinant and a charact…