Let P_0 be an arbitrarily fixed (m, 2s, s)-type subspace of a finite orthogonal geometry with characteristic≠2. Taking as treatments the (1,0,0)-type subspaces of this geometry which are orthogonal to P_0 but not included in P_0, A number of association schemes and PBIB designs with two or three associate classes are constructed.
The paper studies generic commutative and anticommutative algebras of a fixed dimension, their invariants, covariants and algebraic properties (e.g., the structure of subalgebras).
A basis is calledmonomial if each of its elements is the result of applying to a (fixed) highest weight vector a monomial in the Chevalley basis elementsYα, α a simple root, in the opposite Borel subalgebra.
Rational smoothness and fixed points of torus actions
The symmetric varieties considered in this paper are the quotientsG/H, whereG is an adjoint semi-simple group over a fieldk of characteristic ≠ 2, andH is the fixed point group of an involutorial automorphism ofG which is defined overk.
LetMm be a closed smooth manifold with an involution having fixed set of the form (point)?Fn, 0>amp;lt;n>amp;lt;m.