262,270 research outputs found
Kac-Moody symmetric spaces of Euclidean type
We investigate in detail the class of Euclidean affine Kac-Moody symmetric
spaces and their orthogonal symmetric affine Kac-Moody algebras (OSAKAs). These
spaces are the only class of Kac-Moody symmetric spaces, that is not directly
derived from affine Kac-Moody algebras in the classical sense.Comment: arXiv admin note: text overlap with arXiv:1109.283
Birational Weyl group action arising from a nilpotent Poisson algebra
We propose a general method to realize an arbitrary Weyl group of Kac-Moody
type as a group of birational canonical transformations, by means of a
nilpotent Poisson algebra. We also give a Lie theoretic interpretation of this
realization in terms of Kac-Moody Lie algebras and Kac-Moody groups.Comment: 31 pages, LaTe
Integral forms of Kac-Moody groups and Eisenstein series in low dimensional supergravity theories
Kac-Moody groups over have been conjectured to occur as
symmetry groups of supergravities in dimensions less than 3, and their integer
forms are conjecturally U-duality groups. Mathematical
descriptions of , due to Tits, are functorial and not amenable
to computation or applications. We construct Kac-Moody groups over
and using an analog of Chevalley's constructions in finite
dimensions and Garland's constructions in the affine case. We extend a
construction of Eisenstein series on finite dimensional semisimple algebraic
groups using representation theory, which appeared in the context of
superstring theory, to general Kac-Moody groups. This coincides with a
generalization of Garland's Eisenstein series on affine Kac-Moody groups to
general Kac-Moody groups and includes Eisenstein series on and
. For finite dimensional groups, Eisenstein series encode the quantum
corrections in string theory and supergravity theories. Their Kac-Moody analogs
will likely also play an important part in string theory, though their roles
are not yet understood
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