Commensurabilities among Lattices in PU (1,n)
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A01=G. Daniel Mostow
A01=George Daniel Mostow
A01=Pierre R. Deligne
Algebraic variety
Analytic continuation
Arithmetic group
Author_G. Daniel Mostow
Author_George Daniel Mostow
Author_Pierre R. Deligne
Automorphism
Bernhard Riemann
Category=PBF
Category=PBG
Codimension
Coefficient
Cohomology
Commensurability (mathematics)
Compactification (mathematics)
Complete quadrangle
Complex number
Complex space
Conjugacy class
Connected component (graph theory)
Coprime integers
Cube root
Derivative
Diagonal matrix
Differential equation
Dimension (vector space)
Discrete group
Divisor
Divisor (algebraic geometry)
Eigenvalues and eigenvectors
Ellipse
Elliptic curve
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Equation
Existential quantification
Fiber bundle
Finite group
First principle
Fundamental group
Holomorphic function
Hypergeometric function
Hypersurface
Integer
Inverse function
Irreducible component
Irreducible representation
Line bundle
Linear combination
Linear differential equation
Local system
Locally finite collection
Mathematical proof
Minkowski space
Moduli space
Monodromy
Multiplicative group
Neighbourhood (mathematics)
Open set
Orbifold
Permutation
Picard group
Point at infinity
Polynomial ring
Projective line
Projective plane
Projective space
Root of unity
Second derivative
Subset
Symmetry group
Tangent
Theorem
Transversal (geometry)
Uniqueness theorem
Variable (mathematics)
Vector space
Product details
- ISBN 9780691000961
- Weight: 28g
- Dimensions: 197 x 254mm
- Publication Date: 12 Sep 1993
- Publisher: Princeton University Press
- Publication City/Country: US
- Product Form: Paperback
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The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions.
The characterization of hypergeometric-like functions by their exponents at the divisors "at infinity" permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable.
Pierre Deligne is a Permanent Member of the Department of Mathematics at the Institute for Advanced Study in Princeton. G. Daniel Mostow is Henry Ford II Professor of Mathematics at Yale University.
