相关论文: Shading A-polynomials via huge representations of …

This paper investigates the relation between colored HOMFLY-PT and Kauffman homology, $\text{SO}(N)$ quantum $6j$-symbols and $(a,t)$-deformed $F_K$. First, we present a simple rule of grading change which allows us to obtain the…

The generalization of 4D confining string theory to the SU(3)-inspired case is derived. It describes string representation of the Wilson loop in the SU(3)-analogue of compact QED extended by the $\theta$-term. It is shown that although the…

Starting with the usual definitions of octonions, an attempt has been made to establish the relations between octonion basis elements and Gell-Mann \lambda matrices of SU(3)symmetry on comparing the multiplication tables for Gell-Mann…

Polynomial relations for generators of $su(2)$ Lie algebra in arbitrary representations are found. They generalize usual relation for Pauli operators in spin 1/2 case and permit to construct modified Holstein-Primakoff transformations in…

For each infinite series of the classical Lie groups of type B,C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in…

In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the…

Kirillov and Naruse have constructed double Grothendieck polynomials to represent the equivariant K-theory classes of Schubert varieties in the complete flag manifolds of types B, C, and D. We derive a recursive formula for these…

In this paper, we propose and discuss implications of a general conjecture that there is a canonical action of a rank 1 double affine Hecke algebra on the Kauffman bracket skein module of the complement of a knot $K \subset S^3$. We prove…

This article is devoted to the computation of Jack connection coefficients, a generalization of the connection coefficients of two classical commutative subalgebras of the group algebra of the symmetric group: the class algebra and the…

Recently developed general constraint polynomial approach is shown to replace a set of algebraic equations of the functional Bethe Ansatz method by a single polynomial constraint. As the proof of principle, the usefulness of the method is…

An explicit formula for the $A$-polynomial of the knot with Conway's notation $C(2n,3)$ is obtained from the explicit Riley-Mednykh polynomial of it.

We study q-holonomic sequences that arise as the colored Jones polynomial of knots in 3-space. The minimal-order recurrence for such a sequence is called the (non-commutative) A-polynomial of a knot. Using the "method of guessing", we…

We show that from the asymptotic behavior of an evaluation of the colored Jones polynomial of the figure-eight knot we can extract the Chern--Simons invariant and the twisted Reidemeister torsion associated with a representation of the…

To a singular knot K with n double points, one can associate a chord diagram with n chords. A chord diagram can also be understood as a 4-regular graph endowed with an oriented Euler circuit. L. Traldi introduced a polynomial invariant for…

We introduce shifted analogues of key polynomials related to symplectic and orthogonal orbit closures in the complete flag variety. Our definitions are given by applying isobaric divided difference operators to the analogues of Schubert…

In the present paper, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of orthogonal polynomials are provided based on 2-parameters weight functions. Such classes englobe the well…

In this paper, we review a new approach to study subalgebra chains $\mathfrak{g} \supset \mathfrak{g}'$ in the context of nuclear physics. This approach does not rely on explicit realizations as bosons or differential operators. We rely on…

Semiholomorphic polynomials are functions $f:\mathbb{C}^2\to\mathbb{C}$ that can be written as polynomials in complex variables $u$, $v$ and the complex conjugate $\overline{v}$. We prove the semiholomorphic analogoue of Akbulut's and…

We develop algebro-combinatorial tools for computing the Thom polynomials for the Morin singularities $A_i(-)$ ($i\ge 0$). The main tool is the function $F^{(i)}_r$ defined as a combination of Schur functions with certain numerical…

Kantor and Trishin described the algebra of polynomial invariants of the adjoint representation of the Lie supergalgebra $gl(m|n)$ and a related algebra $A_s$ of what they called pseudosymmetric polynomials over an algebraically closed…