Vaso, Laertis

One of the most useful tools in representation theory of algebras is Auslander–Reiten theory. A higher dimensional analogue has recently appeared, based on the notion of n-cluster tilting subcategories. It turns out that the existence of such subcategories in the module category of an algebra gives important information about the whole module categ...

Faitg, Matthieu

The algebras L(g,n,H) have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the middle of the 1990's, in the program of combinatorial quantization of the moduli space of flat G-connections over the surface S(g,n) of genus g with n open disks removed. The Hopf algebra H, called gauge algebra, was originally the quantum group U_q(g...

Martin-Dussaud, Pierre
Published in
General Relativity and Gravitation

Calculations in Loop Quantum Gravity (LQG) and spin-foams theory rely heavily on group theory of SU(2) and SL2(C)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$SL_{2}(...

Law, Stacey Wing Chee

In this thesis, we study the representation theory of the symmetric groups $\mathfrak{S}_n$, their Sylow $p$-subgroups $P_n$ and related algebras. For all primes $p$ and natural numbers $n$, we determine the maximum number of distinct irreducible constituents of degree coprime to $p$ of restrictions of irreducible characters of $\mathfrak{S}_n$ to ...

van der Toorn, R. (author)

We revisit Rossby-Haurwitz planetary wave modes of a two-dimensional fluid along the surface of a rotating planet, as elements of irreducible representations of the so(3) Lie algebra. Key questions addressed are, firstly, why it is that the non-linear self-interaction of any Rossby-Haurwitz wave mode is zero, and secondly,

why the phase velocity of ...

Cardona, Duván
Published in
Journal of Pseudo-Differential Operators and Applications

In this note we study the analytical index of pseudo-differential operators by using the notion of (infinite dimensional) operator-valued symbols (in the sense of Ruzhansky and Turunen). Our main tools will be the McKean–Singer index formula together with the operator-valued functional calculus developed here.

Recker, Jan Christof Green, Peter

When analyzing or designing information systems, users often work with multiple conceptual models because each model articulates a different, partial aspect of a real-world domain. However, the available research in this area has largely studied the use of single modeling artifacts only. We develop a new theory about interpreting multiple conceptua...

Recker, Jan Indulska, Marta Green, Peter Burton-Jones, Andrew Weber, Ron

Representation Theory proposes that the basic purpose of an information system (IS) is to faithfully represent certain real-world phenomena, allowing users to reason about these phenomena more cost-effectively than if they were observed directly. Over the past three decades, the theory has underpinned much research on conceptual modeling in IS anal...

Pasquali, Andrea

This thesis consists of an introduction and five research articles about representation theory of algebras. Papers I and II focus on the tensor product of algebras from the point of view of higher-dimensional Auslander-Reiten theory. In Paper I we consider the tensor product Λ of two algebras which are n- respectively m-representation finite. In th...

Habib, Michel Nourine, Lhouari

This paper proposes a representation theory for any finite lattice via set-colored posets, in the spirit of Birkhoff for distributive lattices. The notion of colored posets was introduced in Nourine (2000) [34] and the generalization to set-colored posets was given in Nourine (2000) [35]. In this paper, we give a characterization of set-colored pos...