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Concept

Affine Lie algebra

Related publications (20)

Cohomology in singular blocks of parabolic category O

Jonathan Gruber

We determine the dimensions of Ext -groups between simple modules and dual generalized Verma modules in singular blocks of parabolic versions of category O for complex semisimple Lie algebras and affine Kac-Moody algebras. ...

2023

On minimal tilting complexes in highest weight categories

Jonathan Gruber

We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...

2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure

Clément Hongler

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...

SPRINGER2022

Remarks on the derived center of small quantum groups

Anna Lachowska

Let u(q)(g) be the small quantum group associated with a complex semisimple Lie algebra g and a primitive root of unity q, satisfying certain restrictions. We establish the equivalence between three different actions of g on the center of u(q)(g) and on th ...

SPRINGER INTERNATIONAL PUBLISHING AG2021

Orders That Are Etale-Locally Isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat etale R-algebra are isomorphic. On the other hand, ...

AMER MATHEMATICAL SOC2020

Orders that are étale-locally isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

2019

Petersson inner products of weight-one modular forms

Maryna Viazovska

In this paper we study the regularized Petersson product between a holomorphic theta series associated to a positive definite binary quadratic form and a weakly holomorphic weight-one modular form with integral Fourier coefficients. In [18], we proved that ...

2019

The Center of Small Quantum Groups I: The Principal Block in Type A

Anna Lachowska

We develop an elementary algebraic method to compute the center of the principal block of a small quantum group associated with a complex semisimple Lie algebra at a root of unity. The cases of sl(3) and sl(4) are computed explicitly. This allows us to for ...

OXFORD UNIV PRESS2018

Toda frames, harmonic maps and extended Dynkin diagrams

Katharine Felicity Turner

We consider a natural subclass of harmonic maps from a surface into G/T, namely cyclic primitive maps. Here G is any simple real Lie group (not necessarily compact), T is a Cartan subgroup and both are chosen so that there is a Coxeter automorphism on G(C) ...

Elsevier2017

Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Tudor Ratiu

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 -245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quas ...

Taylor & Francis Ltd2016

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...

EPFL2016

Integrable Systems of Neumann Type

Tudor Ratiu

We construct families of integrable systems that interpolate between -dimensional harmonic oscillators and Neumann systems. This is achieved by studying a family of integrable systems generated by the Casimir functions of the Lie algebra of real skew-symme ...

Springer Verlag2015

Positivity for Kac polynomials and DT-invariants of quivers

Tamás Hausel

We give a cohomological interpretation of both the Kac polynomial and the refined Donaldson-Thomas-invariants of quivers. This interpretation yields a proof of a conjecture of Kac from 1982 and gives a new perspective on recent work of Kontsevich Soibelman ...

Annal Mathematics2013

L-2-Betti numbers of locally compact groups

Henrik Densing Petersen

The present paper is a summary and overview of results obtained in the author's thesis, "L-2-Betti Numbers of Locally Compact Groups", wherein the definition of L-2-Betti numbers for countable groups is extended to locally compact unimodular groups. In man ...

Elsevier2013

The dilaton Wess-Zumino action in higher dimensions

Boaz Keren Zur

We present a general formula for the Wess-Zumino action associated with the Weyl anomaly, given in a curved background for any even number of dimensions. The result is obtained by considering a finite Weyl transformation of counterterms in dimensional regu ...

Springer Nature2013

Carving out the space of 4D CFTs

Alessandro Vichi

We introduce a new numerical algorithm based on semidefinite programming to efficiently compute bounds on operator dimensions, central charges, and OPT coefficients in 4D conformal and N = 1 superconformal field theories. Using our algorithm, we dramatical ...

Springer Nature2012

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

A new approach for computationally efficient estimation of stability factors for parametric partial differential equations is presented. The general parametric bilinear form of the problem is approximated by two affinely parametrized bilinear forms at diff ...

EDP Sciences2012

Descent properties of hermitian Witt groups in inseparable extensions

Eva Bayer Fluckiger, Daniel Arnold Moldovan

Let k be a field of characteristic ≠2, A be a central simple algebra with involution σ over k and W(A,σ) be the associated Witt group of hermitian forms. We prove that for all purely inseparable extensions L of k, the canonical map rL/k:W(A,σ)⟶W(AL,σL) is ...

Springer Verlag2011

Système de poids sur une algèbre de Lie nilpotente

Let g be a nilpotent Lie algebra (of finite dimension n over an algebraically closed field of characteristic zero) and let Der(g) be the algebra of derivations of g. The system of weights of g is defined as being that of the standard representation of a "m ...

s.n.1973

Related publications (20)

Cohomology in singular blocks of parabolic category O

Jonathan Gruber

2023

On minimal tilting complexes in highest weight categories

Jonathan Gruber

2022

A Hopf algebra model for Dwyer's tame spaces

Haoqing Wu

In this thesis, we give a modern treatment of Dwyer's tame homotopy theory using the language of

\infty

-categories. We introduce the notion of tame spectra and show it has a concrete algebraic description. We then carry out a study of

\infty

-operads an ...

EPFL2022

Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure

Clément Hongler

SPRINGER2022

Remarks on the derived center of small quantum groups

Anna Lachowska

SPRINGER INTERNATIONAL PUBLISHING AG2021

Orders That Are Etale-Locally Isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

AMER MATHEMATICAL SOC2020

Orders that are étale-locally isomorphic

Eva Bayer Fluckiger, Mathieu Huruguen

Let R be a semilocal Dedekind domain with fraction field F. It is shown that two hereditary R-orders in central simple F-algebras that become isomorphic after tensoring with F and with some faithfully flat étale R-algebra are isomorphic. On the other hand, ...

2019

On the approximation of stability factors for general parametrized partial differential equations with a two-level affine decomposition

Gianluigi Rozza, Andrea Manzoni, Toni Mikael Lassila

EDP Sciences2012

Descent properties of hermitian Witt groups in inseparable extensions

Eva Bayer Fluckiger, Daniel Arnold Moldovan

Springer Verlag2011

Système de poids sur une algèbre de Lie nilpotente

s.n.1973