Javier Méndez | Searcharxiv

arXiv2026

The monoidal structure of the category of partial representations of finite groups

In this work, we analyze the structure of the category of partial representations of a finite group $G$ as a multifusion category, providing an alternative way to describe simple objects and their tensor products. We describe the interconnection between the category of partial representations of a finite group and the category of global representations of its subgroups (the Christmas Tree's Theorem). Also, for a finite abelian group $G$, we prove that the category of partial representations of any of its subgroups can be embedded into the category of partial representations of $G$ (the Matryoshka's Theorem).

math.RT↗

arXiv2018

Tycho's supernova: the view from {\it Gaia}

SN 1572 (Tycho Brahe's supernova) clearly belongs to the Ia (thermonuclear) type. It was produced by the explosion of a white dwarf in a binary system. Its remnant has been the first of this type to be explored in search of a possible surviving companion, the mass donor that brought the white dwarf to the point of explosion. A high peculiar motion with respect to the stars at the same location in the Galaxy, mainly due to the orbital velocity at the time of the explosion, is a basic criterion for the detection of such companions. Radial velocities from the spectra of the stars close to the geometrical center of Tycho's supernova remnant, plus proper motions of the same stars, obtained by astrometry with the {\it Hubble Space Telescope}, have been used so far. In addition, a detailed chemical analysis of the atmospheres of a sample of candidate stars had been made. However, the distances to the stars, remained uncertain. Now, the Second {\it Gaia} Data Release (DR2) provides unprecedent accurate distances and new proper motions for the stars can be compared with those made from the {\it HST}. We consider the Galactic orbits that the candidate stars to SN companion would have in the future. We do this to explore kinematic peculiarity. We also locate a representative sample of candidate stars in the Toomre diagram. Using the new data, we reevaluate here the status of the candidates suggested thus far, as well as the larger sample of the stars seen in the central region of the remnant.

astro-ph.SR↗