Related papers: Shintani's invariant via cyclic quantum dilogarith…

This is my PhD thesis supervised by Professor Jerzy Weyman. A symmetric quiver $(Q,\sigma)$ is a finite quiver without oriented cycles $Q=(Q_0,Q_1)$ equipped with a contravariant involution $\sigma$ on $Q_0\sqcup Q_1$. The involution allows…

We study hyperbolic polynomials with nice symmetry and express them as the determinant of a Hermitian matrix with special structure. The goal of this paper is to answer a question posed by Chien and Nakazato in 2015. By properly modifying a…

We show that the quantum invariants arising from typical representations of the quantum group $U_h\mathfrak{sl}(2|1)$ are q-holonomic. In particular, this implies the existence of an underlying field theory for which this family of…

Starting from the bi-local Klein-Gordon Equation with spin-independent squared-mass operator, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this…

Using Dunkl operators, we introduce a continuous family of canonical invariants of finite reflection groups. We verify that the elementary canonical invariants of the symmetric group are deformations of the elementary symmetric polynomials.…

Given a 3-cocycle $\psi$ in the cohomology of a finite group $G$, we can define the Dijkgraaf-Witten invariant of closed 3-manifolds. In this paper, we focus on the case where $\psi$ is a 3-cocycle canonically obtained from the second Chern…

We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum…

We consider full perturbations to a covariantly defined Schwarzschild spacetime. By constructing complex quantities, we derive two decoupled, covariant and gauge-invariant, wave-like equations for spin-weighted scalars. These arise…

In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski…

In this note, we give an exposition of the construction of Seiberg-Witten invariants.

Assuming the spin-independence for confining force, we give a covariant quark representation of general composite meson systems with definite Lorentz transformation properties. For benefit of this representation we are able to deduce…

In 1994, Witten has defined a monopole invariant and he has shown the equivalence of this invariant with Donaldson's polynomial using his result in \( \SS \)-duality. This new invariant is very powerful because the gauge group is abelian.…

In this paper, we find the invariant for $n$-qubits and propose the residual entanglement for $n$-qubits by means of the invariant. Thus, we establish a relation between SLOCC entanglement and the residual entanglement. The invariant and…

Using the curved bc-beta-gamma system (a tensor product of a Heisenberg and a Clifford vertex algebra) we introduce quantum analogy of Lichnerowicz differential. As follows we suggest new machinery for finding the Lichnerowicz-Poisson…

Using the theory of representations of the symmetric group, we propose an algorithm to compute the invariant ring of a permutation group. Our approach have the goal to reduce the amount of linear algebra computations and exploit a thinner…

Symbol is used to describe the Springer correspondence for the classical groups. We prove two structure theorems of symbol. We propose a construction of the symbol of the rigid partitions in the $B_n$, $C_n$, and $D_n$ theories. This…

Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…

We prove an analogue of the Lagrange Inversion Theorem for Dirichlet series. The proof is based on studying properties of Dirichlet convolution polynomials, which are analogues of convolution polynomials introduced by Knuth in [4].

A Feynman period is a particular residue of a scalar Feynman integral which is both physically and number theoretically interesting. Two ways in which the graph theory of the underlying Feynman graph can illuminate the Feynman period are…

In the paper we introduce the construction of invariants for 3-manifolds, based on the same key concepts as the classical Dijkgraaf-Witten invariant. We introduce the notion of a special $G$-system and describe how each system induces the…