Related papers: Spin Calogero-Moser models on symmetric spaces

We construct integrable generalizations of the elliptic Calogero-Sutherland-Moser model of particles with spin, involving noncommutative spin interactions. The spin coupling potential is a modular function and, generically, breaks the…

In this note, we establish several interesting connections between the supergroup gauge theories and the super integrable systems, i.e. gauge theories with supergroups as their gauge groups and integrable systems defined on superalgebras.…

We show how the elliptic Calogero-Moser integrable systems arise from a symplectic quotient construction, generalising the construction for A_{N-1} by Gorsky and Nekrasov to other algebras. This clarifies the role of (twisted) affine…

We present the analogue, for an arbitrary complex reductive group G, of the elliptic integrable systems of Sklyanin. The Sklyanin integrable systems were originally constructed on symplectic leaves, of a quadratic Poisson structure, on a…

We introduce the symplectic group $\mathrm{Sp}_2(G, \sigma)$ associated to a Lie subgroup $G$ of a (possibly noncommutative) associative algebra $A$ equipped with an anti-involution $\sigma$. Our construction recovers several classical Lie…

Let G be a split real Kac-Moody group of arbitrary type and let K be its maximal compact subgroup, i.e. the subgroup of elements fixed by a Cartan-Chevalley involution of G. We construct non-trivial spin covers of K, thus confirming a…

This paper is devoted to the construction of new integrable quantum mechanical models based on certain subalgebras of the half loop algebra of gl(N). Various results about these subalgebras are proven by presenting them in the notation of…

The reductions of the free geodesic motion on a non-compact simple Lie group G based on the $G_+ \times G_+$ symmetry given by left- and right multiplications for a maximal compact subgroup $G_+ \subset G$ are investigated. At generic…

Let G be a split semi-simple algebraic group over Q. Let S be a decorated surface, that is a topological oriented surface with a finite set of marked points on the boundary, considered modulo isotopy. We introduce a moduli space D(G,S) and…

We develop a bundle picture for the case that the configuration manifold has only a single isotropy type, and give a formula for the reduced symplectic form in this setting. Furthermore, as an application of this bundle picture we consider…

${\rm SU}(2|1)$ supersymmetric multi-particle quantum mechanics with additional semi-dynamical spin degrees of freedom is considered. In particular, we provide an $\mathcal{N}{=}\,4$ supersymmetrization of the quantum ${\rm U}(2)$ spin…

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a classical Calogero model by a subset of its discrete symmetries. Such reductions reproduce all known variants of these systems, including some…

We review recent results on new physical models constructed as PT-symmetrical deformations or extensions of different types of integrable models. We present non-Hermitian versions of quantum spin chains, multi-particle systems of…

The theory of representations of quivers and of their preprojective algebras are reviewed. In particular, moduli spaces of representations of these algebras, quiver varieties and reflection functor are described. The proof that the…

We study spin structures on affine Kac-Moody symmetric spaces and obtain sufficient conditions for their existence.\ As a by product of this, we obtain a spin-c representation of certain Kac-Moody quadratic subgroups of type E.

Recent well-posedness results have identified the Hardy space $L^2_+$ as the natural phase space for continuum Calogero-Moser models, both focusing and defocusing, on the line and on the torus. In this paper, we introduce a symplectic form…

The main result of this paper is an explicit description of the stratification of the phase space of Calogero--Moser--Sutherland (CMS) integrable systems corresponding to Lie groups $SU(n)$. The phase space decomposes into symplectic strata…

A classification is given of the exceptional $\mathbb{Z}_2 \times \mathbb{Z}_2$-symmetric spaces $G/K$ by A.Kollross, where $G$ is an exceptional compact Lie group or $S\!pin(8)$, and moreover the structure of $K$ is determined as Lie…

For a connected reductive group $G_k$ over an algebraically closed field $k$ of char $\neq 2$ and a fixed point subgroup $K_k$ under an algebraic group involution, we construct a quantization and an integral model of any affine embeddings…

We present a brief account of a series of recent results on twisted and untwisted elliptic Calogero-Moser systems, and on their fundamental role in the Seiberg-Witten solution of gauge theories with one massive hypermultiplet in the adjoint…