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Algebraic loop groups and moduli spaces of bundles

Gerd Faltings (2003)

Journal of the European Mathematical Society

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.

Semibounded Unitary Representations of Double Extensions of Hilbert–Loop Groups

K. H. Neeb (2014)

Annales de l’institut Fourier

A unitary representation π of a, possibly infinite dimensional, Lie group G is called semibounded if the corresponding operators i d π ( x ) from the derived representation are uniformly bounded from above on some non-empty open subset of the Lie algebra 𝔤 of G . We classify all irreducible semibounded representations of the groups ^ φ ( K ) which are double extensions of the twisted loop group φ ( K ) , where K is a simple Hilbert–Lie group (in the sense that the scalar product on its Lie algebra is invariant) and φ is...

The symplectic Kadomtsev-Petviashvili hierarchy and rational solutions of Painlevé VI

Henrik Aratyn, Johan van de LEUR (2005)

Annales de l’institut Fourier

Equivalence is established between a special class of Painlevé VI equations parametrized by a conformal dimension μ , 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...

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