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$A_1$-type subgroups containing regular unipotent elements

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Multiplicity-free Representations of Algebraic Groups

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Multimodal transcriptomic atlases of mouse spinal cord injury

Matthieu Pierre Gautier

A spinal cord injury (SCI) triggers a cascade of molecular and cellular responses involving inflammatory cell infiltration and cytokine release, apoptosis, demyelination, excitotoxicity, ischemia, and the formation of a fibrotic scar surrounded by an astro ...

EPFL2024

When Subtyping Constraints Liberate A Novel Type Inference Approach for First-Class Polymorphism

Lionel Emile Vincent Parreaux, Aleksander Slawomir Boruch-Gruszecki

Type inference in the presence of first-class or "impredicative" second-order polymorphism a la System F has been an active research area for several decades, with original works dating back to the end of the 80s. Yet, until now many basic problems remain ...

Assoc Computing Machinery2024

Lie groups in the symmetric group: Reducing Ulam's problem to the simple case

Nicolas Monod

Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...

Academic Press Inc Elsevier Science2023

Unlikely intersections on the p-adic formal ball

Vlad Serban

We investigate generalizations along the lines of the Mordell-Lang conjecture of the author's p-adic formal Manin-Mumford results for n-dimensional p-divisible formal groups F. In particular, given a finitely generated subgroup (sic) of F(Q(p)) and a close ...

SPRINGER INT PUBL AG2023

Between the Pattern and the Type: A short parallel story

Vasileios Chanis

Historically speaking, the notion of the type was reintroduced to the larger architectural discourse as a direct consequence of the crisis of the Modern. The task of revisiting the forms of the past also dictated the return of architectural methods that ha ...

2023

Disagreement and fragmentation in growing groups

Jiyong Zhang, Yubo Xie

The arise of disagreement is an emergent phenomenon that can be observed within a growing social group and, beyond a certain threshold, can lead to group fragmentation. To better understand how disagreement emerges, we introduce an analytically tractable m ...

PERGAMON-ELSEVIER SCIENCE LTD2023

A DONALDSON-THOMAS CREPANT RESOLUTION CONJECTURE ON CALABI-YAU 4-FOLDS

Sergej Monavari

Let G be a finite subgroup of SU(4) such that its elements have age at most one. In the first part of this paper, we define K-theoretic stable pair invariants on a crepant resolution of the affine quotient C4/G, and conjecture a closed formula for their ge ...

Amer Mathematical Soc2023

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

Regulation and function of a hemicleaved Activin-A processing intermediate in melanoma

Manon Bulliard

Activin-A is a Transforming Growth Factor-B (TGFB)-related cytokine that regulates various biological processes including cell proliferation and differentiation through autocrine, paracrine or endocrine signaling. Activin-A expression is upregulated in mul ...

EPFL2023

Capturing Types

Martin Odersky, Ondrej Lhoták, Aleksander Slawomir Boruch-Gruszecki

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CC

Assoc Computing Machinery2023

Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

Ana-Maria Retegan

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

EPFL2022

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

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

Multiplicity-free representations of algebraic groups II

Donna Testerman, Martin W. Liebeck

We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Lie groups as permutation groups: Ulam's problem in the nilpotent case

Nicolas Monod

Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...

WALTER DE GRUYTER GMBH2022

Studies on Types: Dormitories

Estelle Lépine, Tiago André Pratas Borges, Anja Fröhlich, Vanessa Pointet

Concepts of type and typology are not specific to architecture. Rather they represent an interdisciplinary approach to ordering knowledge and gaining insight. In the field of architecture, the study of types and typology offers a didactic perspective that ...

EPFL Press2022

An Exploratory Study of Reactions to Bot Comments on GitHub

Denis Gillet, Sandy Ingram, Juan Carlos Farah, Xinyang Lu

The widespread use of bots to support software development makes social coding platforms such as GitHub a particularly rich source of data for the study of human-bot interaction. Software development bots are used to automate repetitive tasks, interacting ...

ACM2022

The concept of axial weak twins

Cyril Cayron

It is generally assumed that the parent-twin interface is a fully invariant plane. The calculations of the rational interfaces of the type I twins and irrational interfaces of the type II twins are based on this hypothesis. Recently, some asymmetric facets ...

PERGAMON-ELSEVIER SCIENCE LTD2022

Invariant integrals on topological groups

Vasco Schiavo

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in [23] to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we look at the class of gro ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

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