arXiv subjects

Ayan Dey

Publications and source records attributed to Ayan Dey.

6 recordsLinked to original sources

arXiv2026

Generalized Quantum Minors Generate Quantized Coordinate Rings

Let $G$ be a simply connected simple complex algebraic group. It is proved by Oya, Qin, and Yakimov that the quantized coordinate ring $\mathcal{O}_q(G)$ is generated by generalized quantum minors, and therefore carries a quantized cluster algebra structure, for all $G$ but type $F_4$. In this article, we settle the $F_4$ case by an argument uniform across $G_2$, $F_4$, and $E_8$. The main idea is to bootstrap the existing proof in type $E_8$, which relies on Lusztig's canonical basis of the quantum adjoint representation, and replace it with the crystal combinatorics of the quasi-minuscule representation. As a consequence, we prove that $\mathcal{O}_q(F_4)$ also has a quantized cluster algebra structure.

math.QA↗

arXiv2026

Triangular Decomposition of the Crystal Lattice of Quantized Function Algebras: Exceptional Types

For $\g$ of type $G_2$, $F_4$, or $E_8$, let $G$ be the connected simply connected complex Lie group with $\mathrm{Lie}(G)=\g$, and compact real form $K$. We prove the triangular decomposition $\OAztG=A_0\text{-alg}\!<\RAzp \cup \RAzm>$ of the crystal lattice of $\OtG$. Together with~\cite{DDPa}, which treats types $A_n$--$D_n$, $E_6$, $E_7$, this settles the triangular decomposition for all simple complex Lie algebras. As a consequence, we obtain the inclusion $\OAztG\subseteq\OAztK$ conjectured by Matassa--Yuncken in full generality, and the crystal limit $\CpKo$ is a compact quantum semigroup with a bounded counit and a unique bi-invariant (Haar) state.

math.QA↗

arXiv2025

A note on the Penrose process in rotating regular black holes

We investigate the Penrose process of energy extraction in the context of rotating regular black holes. For the Neves-Saa class of regular black hole solutions, which includes the Bardeen, Hayward and Fan-Wang spacetimes as special cases, the extraction efficiency is bounded above by the known value for Kerr spacetime. However, in the case of a new rotating regular black hole which does not have a Schwarzschild singular limit for zero rotation, the extraction efficiency can indeed become very large, as shown in our analysis here.

gr-qc↗

arXiv2025

A triangular decomposition for the crystal lattice of quantized function algebras

We prove a triangular decomposition theorem for the lower crystal lattice $\mathcal{O}_{t}^{A_{0}}(G)$ of the quantized function algebra $\mathcal{O}_{t}^{}(G)$, where $G$ is a connected simply connected complex Lie group with Lie algebra $\mathfrak {g}$ of type $A_{n}$, $B_{n}$, $C_{n}$, $D_{n}$, $E_{6}$ or $E_{7}$. As a consequence, we prove the inclusion $\mathcal{O}_{t}^{A_{0}}(G)\subseteq\mathcal{O}_{t}^{A_{0}}(K)$ conjectured by Matassa \& Yuncken in these cases. Using this inclusion, we then prove that the notions of crystallized quantized function algebra given by Matassa \& Yuncken coincide with that of Giri \& Pal.

math.QA↗

arXiv2025

On representations of the crystallization of the quantized function algebra C(SUq(n + 1))

The crystal limit C(K0) of the $q$-family of C*-algebras C(Kq) was introduced by Giri & Pal for all K=SU(n+1), n\geq 2. This article aims to prove that the crystal limits C(K0) have the property that the representations of C(Kq) give rise to the representations of the crystallized algebra C(K0) by sending generators of C(K0) to the limit of (scaled) generators of C(Kq)$ and every representation of C(K0) occurs in this way. This work addresses a question raised by Giri & Pal in \cite{GirPal-2024}. As a consequence, one can realize C(K0) as the C*-algebra generated by the limit operators of faithful representations of C(Kq).

math.OA↗

arXiv2024

Closed strings in a class of pp-wave spacetimes and the memory effect

We study closed string evolution in the pp-wave spacetime assuming different pulse shapes (square and sech-squared) in the exact gravitational wave metric. It is shown that the shape of a circular closed string deforms permanently, after the pulse has departed. The worldsheet geometry also displays characteristic permanent changes caused by the gravitational wave pulse. The above effects collectively demonstrate features akin to what is known as `memory' in gravitational wave physics.

gr-qc↗