Mumford-Tate Groups and Domains: Their Geometry and by Mark Green,Phillip A. Griffiths,Matt Kerr

By Mark Green,Phillip A. Griffiths,Matt Kerr

Mumford-Tate teams are the basic symmetry teams of Hodge concept, a subject matter which rests on the heart of latest complicated algebraic geometry. This booklet is the 1st entire exploration of Mumford-Tate teams and domain names. Containing easy conception and a wealth of latest perspectives and effects, it is going to develop into a necessary source for graduate scholars and researchers.

Although Mumford-Tate teams could be outlined for common constructions, their concept and use so far has generally been within the classical case of abelian kinds. whereas the ebook does study this sector, it specializes in the nonclassical case. the final conception seems to be very wealthy, resembling within the unforeseen connections of finite dimensional and endless dimensional illustration idea of actual, semisimple Lie teams. The authors provide the total type of Hodge representations, an issue that are supposed to develop into a customary within the finite-dimensional illustration thought of noncompact, actual, semisimple Lie teams. in addition they point out that during the longer term, a connection turns out able to be made among Lie teams that admit discrete sequence representations and the examine of automorphic cohomology on quotients of Mumford-Tate domain names via mathematics teams. Bringing jointly complicated geometry, illustration thought, and mathematics, this e-book opens up a clean standpoint on a huge subject.

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