16-dimensional compact projective planes with a large group by Hahl H., Salzmann H.

By Hahl H., Salzmann H.

Show description

Read Online or Download 16-dimensional compact projective planes with a large group fixing two points and two lines PDF

Best symmetry and group books

Aspects of Symmetry: Selected Erice Lectures

This choice of evaluation lectures on subject matters in theoretical excessive power physics has few competitors for readability of exposition and intensity of perception. introduced over the last 20 years on the overseas college of Subnuclear Physics in Erice, Sicily, the lectures support to arrange and clarify fabric the time existed in a stressed kingdom, scattered within the literature.

Structure of Factors and Automorphism Groups (Cbms Regional Conference Series in Mathematics) by Masamichi Takesaki (1983-12-31)

This booklet describes the new improvement within the constitution idea of von Neumann algebras and their automorphism teams. it may be seen as a guided journey to the state-of-the-art.

Additional info for 16-dimensional compact projective planes with a large group fixing two points and two lines

Example text

3. (Mackey Decomposition). Let H and S be subgroups of G, let T be a full set of double coset representatives for (S, H ) in G and let V be a n FaH-module. Then An Invitation to Projective Characters 44 Proof. Let { g l , . . ,gn} be a left tra,nsversal for H in G. Then VG = $r=lgg; 8 V (direct sum of F-spaces) Put X = {g; €4 V11 5 i 5 n}. Then G and, in particular S , acts on X . Moreover, gi @ V and g j 8 V lie in the same S-orbit if and only if gi and gj belong to the same double (S, H)-coset.

2(ii), I ( V ) is a subgroup of G containing H . We refer t o I ( V ) as the inertia group of V . If H a G and G = I ( V ) ,then we say that V is G-invariant. If p is an a-representation of H afforded by V , then I ( V ) consists precisely of all those g E N G ( H ) for which p and g p are linearly equivalent If x is the a-character of H afforded by V and g E G , then we write g x for the a-character of gHg-l afforded by g V . We refer to g x as the g-conjugate of x. If gHg-' = H and g x = x , then we say that x is g-invariant.

E. with the case of ordinary characters. Let x be an irreducible a-character of G over F . Assume that F is a splitting field for FOG or that charF = 0. Then the degree of x , written d e g x , is defined to be the F-dimension of a simple FOG-module which affords x. 3, degx is well defined. It is clear that if charF = 0, then d e g x = x(1) 20 An Invitation to Projective Characters Of course, if charF = 0 then we can unambigiously define the degree of an arbitrary a-character x of G over F to be the F-dimension of any F"Gmodule which affords x.

Download PDF sample

Rated 4.80 of 5 – based on 17 votes