Periodicities of T-systems and Y-systems

Abstract

Abstract. The unrestricted T-system is a family of relations in the Grothendieck ring of the category of the finite-dimensional modules of the Yangian or the quantum affine algebra associated with a complex simple Lie algebra. The unrestricted T-system admits a reduction called the restricted T-system. In this paper we formulate the periodicity conjecture for the restricted T-systems, which is the counterpart of the known and partially proved periodicity conjecture for the restricted Y-systems. Then, we partially prove the conjecture by various methods: the cluster algebra and cluster category method for the simply laced case, the determinant method for types A and C, and the direct method for types A, D, and B (level 2).

A Neutral Beam Model for High-energy Neutrino Emission from the Blazar TXS 0506+056

“…We assume that charged particles, including (primary) electrons, protons, and heavier nuclei are accelerated to high energies before they are injected into the blob, where they subsequently lose energy through various radiative processes. Several mechanisms of particle acceleration have been discussed in application to AGN jets, e.g., Fermi type I (Dermer & Razzaque 2010;Inoue & Tanaka 2016), Fermi type II (Böttcher et al 1999;Schlickeiser & Dermer 2000;Katarzynski et al 2006), magnetic reconnection (Lovelace et al 1997;Giannios et al 2009;Nalewajko et al 2018;Christie et al 2019), shear acceleration (Rieger & Duffy 2004;Rieger et al 2007;Kimura et al 2017b). In all scenarios, the acceleration efficiency depends on local plasma conditions (for relativistic shocks in magnetized jets, see Sironi et al 2015a,b).…”

n -representation-finite algebras and twisted fractionally Calabi-Yau algebras

“…The derived categories of finite-dimensional nonsemisimple algebras are never CY, but they are often fractionally CY. Some recent meetings [3,4,39,41] as well as recent results including [16,21,25,27,32,33,[35][36][37][38]42] suggest that the fractionally CY property becomes more and more important in representation theory, singularity theory, commutative and non-commutative algebraic geometry. The aim of this paper is to apply the fractionally CY property in the study of n-representation-finite algebras defined below.…”

Microstructure and Tensile Elongation Enhancement of 1.6 wt% B stainless Steel Plates Fabricated by Composite Rolling

“…Carreño [7] investigated the impact properties of the laminated composite plates consisting of brittle 1.55 wt% C UHCS steel and soft 0.035 wt% C mild steel, indicating that the Charpy V-notched energy of 7-layered laminated composites was 160 kJ m À2 higher than that of the UHCS mono-layered specimens. Inoue [8] prepared the multilayered steel composites consisting of brittle SS420 and relative soft SS304 via hot-roll-bonding, cold rolling and the final heat treated. The results indicated that the fracture elongation enhanced with the decreasing thickness of monolayer and reached to 15% for the specimens with 40 mm-thick per layer.…”