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Keng Wiboonton

Publications and source records attributed to Keng Wiboonton.

13 recordsLinked to original sources
arXiv2026

Quantum Corner Polynomials: A Generalization of Super Macdonald Polynomials and Their VOA Correspondence

In this paper, we introduce a family of partially symmetric polynomials, which we call quantum corner polynomials, as a generalization of the Sergeev-Veselov super Macdonald polynomials. We show that these quantum corner polynomials are precisely the partially symmetric polynomials corresponding to the quantum corner VOAs. Furthermore, we provide a detailed proof of the partial symmetricity of these polynomials.

hep-th↗
arXiv2026

On solvable Lie algebras of small breadth

The concept of breadth has been used in the classification of p-groups and nilpotent Lie algebras. In this paper, we investigate this notion for finite-dimensional solvable Lie algebras. Our main focus is to characterize solvable Lie algebras of breadth less than or equal to 2. More importantly, we provide a complete classification of such Lie algebras that are pure and nonnilpotent over the complex numbers.

math.RA↗
arXiv2025

Quantum Corner VOA and the Super Macdonald Polynomials

In this paper, we establish a relation between the quantum corner VOA $q\widetilde{Y}_{L,0,N}[Ψ]$, which can be regarded as a generalization of quantum $W_N$ algebra, and Sergeev-Veselov super Macdonald polynomials. We demonstrate precisely that, under a specific map, the correlation functions of the currents of $q\widetilde{Y}_{L,0,N}[Ψ]$, coincide with the Sergeev-Veselov super Macdonald polynomials.

hep-th↗
arXiv2025

A recursion formula for Branching from $\mathfrak{sl}_n$ to $\mathfrak{sl}_2$ subalgebras

For any representation of a complex simple Lie algebra $\mathfrak{sl}_n$, one problem of branching rules to $\mathfrak{sl}_2$-subalgebra is to determine the multiplicity of each irreducible component. In this paper, we derive a recursion formula of such multiplicities by restricting a certain tensor representation in two ways, in which the Pieri's rule is involved. We also investigate branching rules for fundamental representations as they are initial conditions of the recursion formula.

math.RT↗
arXiv2024

Elliptic Deformation of the Gaiotto-Rapčák Corner VOA and the Associated Partially Symmetric Polynomials

We construct the elliptic Miura transformation and use it to obtain the expression of the currents of elliptic corner VOA. We subsequently prove a novel combinatorial formula that is essential for deriving the quadratic relations of the currents. In addition, we give a conjecture that relates the correlation function of the currents of elliptic corner VOA to a certain family of partially symmetric polynomials. The elliptic Macdonald polynomials, constructed recently by Awata-Kanno-Mironov-Morozov-Zenkevich, and Fukuda-Ohkubo-Shiraishi, can be obtained as a particular case of this family.

hep-th↗
arXiv2023

More on characteristic polynomials of Lie algebras

In recent years, the notion of characteristic polynomial of representations of Lie algebras has been widely studied. This paper provides more properties of these characteristic polynomials. For simple Lie algebras, we characterize the linearization of characteristic polynomials. Additionally, we characterize nilpotent Lie algebras via characteristic polynomials of the adjoint representation.

math.RT↗
arXiv2017

On the normal centrosymmetric Nonnegative inverse eigenvalue problem

We give sufficient conditions of the nonnegative inverse eigenvalue problem (NIEP) for normal centrosymmetric matrices. These sufficient conditions are analogous to the sufficient conditions of the NIEP for normal matrices given by Xu [16] and Julio, Manzaneda and Soto [2].

math.SP↗
arXiv2017

A characterization of trace zero bisymmetric nonnegative $5 \times 5$ matrices

Let $λ_1 \geq λ_2 \geq λ_3 \geq λ_4 \geq λ_5 \geq -λ_1$ be real numbers such that $\sum_{i=1}^5 λ_i =0$. In \cite{oren}, O. Spector prove that a necessary and sufficient condition for $λ_1, λ_2, λ_3, λ_4, λ_5$ to be the eigenvalues of a symmetric nonnegative $5 \times 5$ matrix is "$λ_2+λ_5<0$ and $\sum_{i=1}^5 λ_{i}^{3} \geq 0"$. In this article, we show that this condition is also a necessary and sufficient condition for $λ_1, λ_2, λ_3, λ_4, λ_5$ to be the spectrum of a traceless bisymmetric nonnegative $5 \times 5$ matrix.

math.RA↗
arXiv2015

On the bisymmetric nonnegative inverse eigenvalue problem

We study the bisymmetric nonnegative inverse eigenvalue problem (BNIEP). This problem is the problem of finding the necessary and sufficient conditions on a list of $n$ complex numbers to be a spectrum of an $n \times n$ bisymmetric nonnegative matrix. Most recently, some of the sufficient conditions for the BNIEP are given by Julio and Soto in 2015. In this article, we give another proof of one result (Theorem 4.3) in [Julio and Soto, 2015] and we obtain the result very similar to the one (Theorem 4.2) in [Julio and Soto, 2015] using a different method to construct our desired bisymmetric nonnegative matrix. We also give some sufficient conditions for the BNIEP based on the sufficient conditions for the nonnegative inverse eigenvalue problem (NIEP) given by Borobia in 1995. We give the condition that is both necessary and sufficient for the BNIEP when $n \leq 4$ and then we show that for $n = 6$, the BNIEP and the symmetric nonnegative eigenvalue problem (SNIEP) are different. Moreover, some sufficient conditions for the bisymmetric positive inverse eigenvalue problem are provided. Finally, we give a new result on a sufficient condition for the BNIEP with the prescribed diagonal entries.

math.SP↗
arXiv2014

Isomorphism Theorems for Gyrogroups and L-Subgyrogroups

We extend well-known results in group theory to gyrogroups, especially the isomorphism theorems. We prove that an arbitrary gyrogroup $G$ induces the gyrogroup structure on the symmetric group of $G$ so that Cayley's Theorem is obtained. Introducing the notion of L-subgyrogroups, we show that an L-subgyrogroup partitions $G$ into left cosets. Consequently, if $H$ is an L-subgyrogroup of a finite gyrogroup $G$, then the order of $H$ divides the order of $G$.

math.GR↗
arXiv2011

The Segal-Bargmann Transform on Compact Symmetric Spaces and their Direct Limits

We study the Segal-Bargmann transform, or the heat transform, $H_t$ for a compact symmetric space $M=U/K$. We prove that $H_t$ is a unitary isomorphism $H_t : L^2(M) \to \cH_t (M_\C)$ using representation theory and the restriction principle. We then show that the Segal-Bargmann transform behaves nicely under propagation of symmetric spaces. If $\{M_n=U_n/K_n,ι_{n,m}\}_n$ is a direct family of compact symmetric spaces such that $M_m$ propagates $M_n$, $m\ge n$, then this gives rise to direct families of Hilbert spaces $\{L^2(M_n),γ_{n,m}\}$ and $\{\cH_t(M_{n\C}),δ_{n,m}\}$ such that $H_{t,m}\circ γ_{n,m}=δ_{n,m}\circ H_{t,n}$. We also consider similar commutative diagrams for the $K_n$-invariant case. These lead to isometric isomorphisms between the Hilbert spaces $\varinjlim L^2(M_n)\simeq \varinjlim \mathcal{H} (M_{n\mathbb{C}})$ as well as $\varinjlim L^2(M_n)^{K_n}\simeq \varinjlim \mathcal{H} (M_{n\mathbb{C}})^{K_n}$.

math.RT↗