Richardson Elements for Parabolic Subgroups of Classical Groups in Positive Characteristic

Richardson Elements for Parabolic Subgroups of Classical Groups in Positive Characteristic

Let G be a simple algebraic group of classical type over an algebraically closed field k. Let P be a parabolic subgroup of G and let p = LieP be the Lie algebra of P with Levi decomposition p = l⊕ u, where u is the Lie algebra of the unipotent radical of P and l is a Levi complement. Thanks to a fundamental theorem of R. W. Richardson ([16]), P acts on u with an open dense orbit; this orbit is ...

Periodic subgroups of projective linear groups in positive characteristic

Received 16 March 2008; accepted 4 May 2008 Abstract: We classify the maximal irreducible periodic subgroups of PGL(q,F) , where F is a field of positive characteristic p transcendental over its prime subfield, q 6= p is prime, and F× has an element of order q . That is, we construct a list of irreducible subgroups G of GL(q,F) containing the centre F×1q of GL(q,F) , such that G/F×1q is a maxim...

AFFINE SUBGROUPS OF THE CLASSICAL GROUPS AND THEIR CHARACTER DEGREES

In this paper we describe how the degrees of the irreducible characters of the affine subgroups of the classical groups under consideration can be found inductively. In [4] Gow obtained certain character degrees for all of the affine subgroups of the classical groups. We apply the method of Fischer to the above groups and, in addition to the character degrees given in [4], we obtain some ne...

Richardson Elements for Classical Lie Algebras

Parabolic subalgebras of semi-simple Lie algebras decompose as p = m⊕ n where m is a Levi factor and n the corresponding nilradical. By Richardsons theorem [R], there exists an open orbit under the action of the adjoint group P on the nilradical. The elements of this dense orbits are known as Richardson elements. In this paper we describe a normal form for Richardson elements in the classical c...

Richardson Orbits for Real Classical Groups