A Cartan decomposition for p-adic loop groups.
A Weierstrass-type representation for harmonic maps from Riemann surfaces to general Lie groups.
Algebraic loop groups and moduli spaces of bundles
We study algebraic loop groups and affine Grassmannians in positive characteristic. The main results are normality of Schubert-varieties, the construction of line-bundles on the affine Grassmannian, and the proof that they induce line-bundles on the moduli-stack of torsors.
Applications exponentielles pour les groupes des courants et la décomposition de Birkhoff pour les groupes des nœuds [Book]
Combinatorial integers and Schubert calculus in the integral cohomology ring of infinite smooth flag manifolds.
Explicit description of a family of affine Kac-Moody groups. (Description explicite d'une famille de groupes de Kac-Moody affines.)
Fusion en algèbres de von Neumann et groupes de lacets
Geometric construction of the classical r-matrix for the elliptic Calogero-Moser system
By applying the Hamiltonian reduction technique we derive a matrix first order differential equation that yields the classical r-matrices of the elliptic (Euler-) Calogero-Moser systems as well as their degenerations.
and operator algebras.
Hecke operators on quasimaps into horospherical varieties.
Homogeneous Poisson structures on loop spaces of symmetric spaces.
Lie groupoids of mappings taking values in a Lie groupoid
Endowing differentiable functions from a compact manifold to a Lie group with the pointwise group operations one obtains the so-called current groups and, as a special case, loop groups. These are prime examples of infinite-dimensional Lie groups modelled on locally convex spaces. In the present paper, we generalise this construction and show that differentiable mappings on a compact manifold (possibly with boundary) with values in a Lie groupoid form infinite-dimensional Lie groupoids which we...
Limit matrices for the Toda flow and periodic flags for loop groups.
Loop group decompositions in the generalized method.
Monstrous moonshine and monstrous Lie superalgebras.
On chiral differential operators over homogeneous spaces.
Profinite and finite groups associated with loop and diffeomorphism groups of non-Archimedean manifolds.
Semibounded Unitary Representations of Double Extensions of Hilbert–Loop Groups
A unitary representation of a, possibly infinite dimensional, Lie group is called semibounded if the corresponding operators from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra of . We classify all irreducible semibounded representations of the groups which are double extensions of the twisted loop group , where is a simple Hilbert–Lie group (in the sense that the scalar product on its Lie algebra is invariant) and is...
The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI
Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension , time dependent Euler top equations, isomonodromic deformations and three-dimensional Frobenius manifolds. The isomonodromic tau function and solutions of the Euler top equations are explicitly constructed in terms of Wronskian solutions of the 2-vector 1-constrained symplectic Kadomtsev-Petviashvili (CKP) hierarchy by means of Grassmannian formulation. These Wronskian solutions give...