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Related papers: Instantons and affine Lie algebras

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We calculate the singular instanton homology with local coefficients for the simplest n-strand braids in $S^1 \times S^2$ for all odd n, describing these homology groups and their module structures in terms of the coordinate rings of…

Geometric Topology · Mathematics 2025-07-02 Peter B. Kronheimer , Tomasz S. Mrowka

We construct a new family of irreducible modules over any basic classical affine Kac-Moody Lie superalgebra which are induced from modules over the Heisenberg subalgebra. We also obtain irreducible deformations of these modules for the…

Representation Theory · Mathematics 2022-02-10 Luan Pereira Bezerra , Lucas Calixto , Vyacheslav Futorny , Iryna Kashuba

In this talk I shall try to give an elementary introduction to certain areas of mathematical physics where the idea of moduli space is used to help solve problems or to further our understanding. In the wide area of gauge theory, I shall…

High Energy Physics - Theory · Physics 2007-05-23 ST Tsou

We prove that Hitchin's generalized Kaehler structure on the moduli space of instantons over a compact, even generalized Kaehler four-manifold may be obtained by generalized Kaehler reduction, in analogy with the usual Kaehler case. The…

Differential Geometry · Mathematics 2023-05-26 Henrique Bursztyn , Gil R. Cavalcanti , Marco Gualtieri

We establish the exponential law for suitably topologies on spaces of vector-valued smooth functions on topological groups, where smoothness is defined by using differentiability along continuous one-parameter subgroups. As an application,…

Functional Analysis · Mathematics 2014-02-26 Daniel Beltita , Mihai Nicolae

We discuss the homological algebra of representation theory of finite dimensional algebras and finite groups. We present various methods for the construction and the study of equivalences of derived categories: local group theory, geometry…

Representation Theory · Mathematics 2007-05-23 Raphael Rouquier

We show that the classical equations of motion of the low-energy effective field theory describing the massless modes of the heterotic (or type I) string admit two classes of supersymmetric self--dual backgrounds. The first class, which was…

High Energy Physics - Theory · Physics 2007-05-23 M. Bianchi , F. Fucito , G. C. Rossi , M. Martellini

This is an old paper put here for archeological purposes. We derive a general formula expressing the second homology of a Lie algebra of the form L\otimes A with coefficients in the trivial module through homology of $L$, cyclic homology of…

K-Theory and Homology · Mathematics 2010-05-18 Pasha Zusmanovich

Algebraic deformations provide a systematic approach to generalizing the symmetries of a physical theory through the introduction of new fundamental constants. The applications of deformations of Lie algebras and Hopf algebras to both…

High Energy Physics - Theory · Physics 2018-05-29 Niels G. Gresnigt , Adam B. Gillard

We study representations of the double affine Lie algebra associated to a simple Lie algebra. We construct a family of indecomposable integrable representations and identify their irreducible quotients. We also give a condition for the…

Quantum Algebra · Mathematics 2007-05-23 Vyjayanthi Chari , Thang Le

In infinite-dimensional Lie theory, the affine Kac-Moody Lie algebras and groups play a distinguished role due to their many applications to various areas of mathematics and physics. Underlying these infinite-dimensional objects there are…

Group Theory · Mathematics 2023-03-22 Jun Morita , Arturo Pianzola , Taiki Shibata

We use the crystal isomorphisms of the Fock space to describe two maps on partitions and multipartitions which naturally appear in the crystal basis theory for quantum groups in affine type A and in the representation theory of Hecke…

Combinatorics · Mathematics 2021-02-24 N Jacon

The results of the paper concern the topological structure of complete riemannian manifolds with cyclic holonomy groups and low-dimensional orientable complete flat manifolds. We also discuss related results such as the affine…

Differential Geometry · Mathematics 2007-05-23 M. Sadowski

A topological version of four-dimensional (Euclidean) Einstein gravity which we propose regards anti-self-dual 2-forms and an anti-self-dual part of the frame connections as fundamental fields. The theory describes the moduli spaces of…

High Energy Physics - Theory · Physics 2011-09-09 Mitsuko Abe , A. Nakamichi , T. Ueno

To any manifold equipped with a higher degree closed form, one can associate an L-infinity algebra of local observables that generalizes the Poisson algebra of a symplectic manifold. Here, by means of an explicit homotopy equivalence, we…

Mathematical Physics · Physics 2014-08-01 Domenico Fiorenza , Christopher L. Rogers , Urs Schreiber

The main purpose of these lecture notes is to provide a concise introduction to Lie groups, Lie algebras, and isometric and adjoint actions, aiming mostly at advanced undergraduate and graduate students. In addition, the connection between…

Differential Geometry · Mathematics 2010-08-31 Marcos M. Alexandrino , Renato G. Bettiol

The notion of an F-manifold algebra is the underlying algebraic structure of an $F$-manifold. We introduce the notion of pre-Lie formal deformations of commutative associative algebras and show that F-manifold algebras are the corresponding…

Rings and Algebras · Mathematics 2021-02-09 Jiefeng Liu , Yunhe Sheng , Chengming Bai

The worldvolume theory of D3-branes probing four D7-branes and an O7-plane on $\mathbb{C}^2/\mathbb{Z}_2$ is given by a supersymmetric USp x USp gauge theory. We demonstrate that, at least for a particular choice of the holonomy at…

High Energy Physics - Theory · Physics 2019-08-19 Yuji Tachikawa

The classical matter fields are sections of a vector bundle E with base manifold M. The space L^2(E) of square integrable matter fields w.r.t. a locally Lebesgue measure on M, has an important module action of C_b^\infty(M) on it. This…

Mathematical Physics · Physics 2014-11-20 Hendrik Grundling , Karl-Hermann Neeb

We study instanton effects along the Coulomb branch of an N=2 supersymmetric Yang-Mills theory with gauge group SU(2) on Asymptotically Locally Euclidean (ALE) spaces. We focus our attention on an Eguchi-Hanson gravitational background and…

High Energy Physics - Theory · Physics 2009-10-30 D. Bellisai , G. Travaglini