AN INDECOMPOSABLE REPRESENTATION AND THE COMPLEX VECTOR SPACE OF HOLOMORPHIC VECTOR FIELDS ON A PSEUDO-HERMITIAN SYMMETRIC SPACE

2019 ◽  
Author(s):  
Nobutaka BOUMUKI
Keyword(s):  
Symmetric Space ◽  
Vector Space ◽  
Vector Fields ◽  
Hermitian Symmetric Space ◽  
Indecomposable Representation ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Holomorphic Vector Fields

scholarly journals Vector fields on certain quotients of complex Stiefel manifolds

2013 ◽  
Vol 63 (4) ◽  
Author(s):  
Shilpa Gondhali ◽  
Parameswaran Sankaran
Keyword(s):  
Vector Space ◽  
Vector Fields ◽  
Scalar Multiplication ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Differentiable Structure ◽  
Stiefel Manifolds ◽  
Cyclic Groups ◽  
Tangent Bundles ◽  
Mod P

AbstractWe consider quotients of complex Stiefel manifolds by finite cyclic groups whose action is induced by the scalar multiplication on the corresponding complex vector space. We obtain a description of their tangent bundles, compute their mod p cohomology and obtain estimates for their span (with respect to their standard differentiable structure). We compute the Pontrjagin and Stiefel-Whitney classes of these manifolds and give applications to their stable parallelizability.

Reflection Subquotients of Unitary Reflection Groups

1999 ◽  
Vol 51 (6) ◽  
pp. 1175-1193 ◽  
Author(s):  
G. I. Lehrer ◽  
T. A. Springer
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Vector Fields ◽  
Reflection Group ◽  
Complex Vector Space ◽  
Reflection Groups ◽  
Complex Vector ◽  
Invariant Vector ◽  
A Finite Group ◽  
Invariant Vector Fields

AbstractLet G be a finite group generated by (pseudo-) reflections in a complex vector space and let g be any linear transformation which normalises G. In an earlier paper, the authors showed how to associate with any maximal eigenspace of an element of the coset gG, a subquotient of G which acts as a reflection group on the eigenspace. In this work, we address the questions of irreducibility and the coexponents of this subquotient, as well as centralisers in G of certain elements of the coset. A criterion is also given in terms of the invariant degrees of G for an integer to be regular for G. A key tool is the investigation of extensions of invariant vector fields on the eigenspace, which leads to some results and questions concerning the geometry of intersections of invariant hypersurfaces.

Linear Symmetry Classes

1976 ◽  
Vol 28 (6) ◽  
pp. 1311-1319 ◽  
Author(s):  
L. J. Cummings ◽  
R. W. Robinson
Keyword(s):  
Vector Space ◽  
Permutation Group ◽  
Cyclic Group ◽  
Symmetry Class ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Linear Character ◽  
Finite Permutation Group ◽  
Symmetry Classes ◽  
Finite Dimensional

A formula is derived for the dimension of a symmetry class of tensors (over a finite dimensional complex vector space) associated with an arbitrary finite permutation group G and a linear character of x of G. This generalizes a result of the first author [3] which solved the problem in case G is a cyclic group.

scholarly journals A note on holomorphic matric automorphic factors with respect to a lattice in a complex vector space

1976 ◽  
Vol 63 ◽  
pp. 163-171 ◽  
Author(s):  
Hisasi Morikawa
Keyword(s):  
Vector Space ◽  
Complex Vector Space ◽  
Complex Vector

A holomorphic n × n-matric automorphic factor with respect to a lattice L in Cg means a system of holomorphic n × n-matrices {μα(z) | α ∈ L} such that

scholarly journals On quasi-permutation representations of finite groups

1994 ◽  
Vol 36 (3) ◽  
pp. 301-308 ◽  
Author(s):  
J. M. Burns ◽  
B. Goldsmith ◽  
B. Hartley ◽  
R. Sandling
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Permutation Group ◽  
Minimal Degree ◽  
Permutation Representation ◽  
Permutation Groups ◽  
Complex Vector Space ◽  
Complex Vector ◽  
Group Situation ◽  
A Finite Group

In [6], Wong defined a quasi-permutation group of degree n to be a finite group G of automorphisms of an n-dimensional complex vector space such that every element of G has non-negative integral trace. The terminology derives from the fact that if G is a finite group of permutations of a set ω of size n, and we think of G as acting on the complex vector space with basis ω, then the trace of an element g ∈ G is equal to the number of points of ω fixed by g. In [6] and [7], Wong studied the extent to which some facts about permutation groups generalize to the quasi-permutation group situation. Here we investigate further the analogy between permutation groups and quasipermutation groups by studying the relation between the minimal degree of a faithful permutation representation of a given finite group G and the minimal degree of a faithful quasi-permutation representation. We shall often prefer to work over the rational field rather than the complex field.

Spinors in Hilbert space

1976 ◽  
Vol 80 (2) ◽  
pp. 337-347 ◽  
Author(s):  
R. J. Plymen
Keyword(s):  
Hilbert Space ◽  
Vector Space ◽  
Orthogonal Group ◽  
Double Cover ◽  
Projective Representation ◽  
Complex Vector Space ◽  
Complex Vector ◽  
True Representation ◽  
Dimension 2 ◽  
Image Position

In 1913, É. Cartan discovered that the special orthogonal groupSO(k) has a ‘two-valued’ representation (i.e. a projective representation) on a complex vector spaceSof dimension 2n, wherek= 2nor 2n+ 1. The projective representation in question lifts to a true representation of the double cover Spin (k) ofSO(k). We restrict attention to the casek= 2n. Under the action of Spin (2n),Sbreaks up into 2 irreducible subspaces:The vectors inSare calledspinors(relative toSO(2n)), those inS+orS−are calledhalf-spinors(4).

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