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Group representation theory. Based on the research semester "Group representation theory", Lausanne, Switzerland, January - June, 2005

Related publications (32)

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Almost cyclic regular semisimple elements in irreducible representations of simple algebraic groups

Donna Testerman

Let G be a simple linear algebraic group defined over an algebraically closed field of characteristic p ≥ 0 and let φ be a nontrivial p-restricted irreducible representation of G. Let T be a maximal torus of G and s ∈ T . We say that s is Ad-regular if α(s ...

2023

Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups

Jonathan Gruber

Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...

AMER MATHEMATICAL SOC2022

Atomic length in Weyl groups

Thomas Gerber

We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the properties of the ...

2022

These notes cover the lectures of the first named author at 2021 IHES Summer School on "Enumerative Geometry, Physics and Representation Theory" with additional details and references. They cover the definition of Khovanov-Rozansky triply graded homology, ...

WILEY2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Irvsp: To obtain irreducible representations of electronic states in the VASP

Quansheng Wu, Ziyi Wang

We present an open-source program irvsp, to compute irreducible representations of electronic states for all 230 space groups with an interface to the Vienna ab-initio Simulation Package. This code is fed with plane-wave-based wavefunctions (e.g. WAVECAR) ...

ELSEVIER2021

Inducing Meaningful Units from Character Sequences with Slot Attention

James Henderson, Melika Behjati

Characters do not convey meaning, but sequences of characters do. We propose an unsupervised distributional method to learn the abstract meaning-bearing units in a sequence of characters. Rather than segmenting the sequence, this model discovers continuous ...

2021

We study the spectra of non-regular semisimple elements in irreducible representations of simple algebraic groups. More precisely, we prove that if G is a simply connected simple linear algebraic group and φ : G → GL(V ) is a non-trivial irreducible repres ...

2021

Irreducible Subgroups of Simple Algebraic Groups – A Survey

Donna Testerman

Let G be a simple linear algebraic group over an algebraically closed field K of characteristic p≥ 0, let H be a proper closed subgroup of G and let V be a nontrivial finite dimensional irreducible rational KG-module. We say that (G,H, V) is an irreducible ...

Cambridge University Press2019

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The book contains extended versions of seven short lecture courses given during a semester programme on Local Representation Theory and Simple Groups, held at the Centre Interfacultaire Bernoulli of the EPF Lausanne. These courses focused on modular repres ...

European Mathematical Society2018