Introduction: Diagnosis of orbital foreign body (FB) penetration is usually obvious when part of the FB is still attached at the entry wound (1). However, the depth and course of the FB in this case was not visible.   Case Report: A 5-year old female presented with a pencil penetrating the left orbit. A computed tomography (CT) scan showed that the pencil penetrated the left orbit (extraseptal)...

In 1986, George Lusztig stated some interesting properties of character sheaves with non-zero restriction to the unipotent variety and proved them for the group SO2n+1(Fq) under the assumption that the characteristic p of Fq is good. In February 1992, the author has given lectures on that proof of Lusztig in the Seminar “Faisceaux Caractères” at the École Normale Supérieure and it was no doubt ...

Let G be a connected reductive algebraic group defined over the finite field Fq , where q is a power of a good prime for G. We write F for the Frobenius morphism of G corresponding to the Fq-structure, so that GF is a finite group of Lie type. Let P be an F -stable parabolic subgroup of G and let U be the unipotent radical of P . In this paper, we prove that the number of UF -conjugacy classes ...

Let G be an algebraic group over a field k. We call g ∈ G(k) real if g is conjugate to g−1 in G(k). In this paper we study reality for groups of type G2 over fields of characteristic different from 2. Let G be such a group over k. We discuss reality for both semisimple and unipotent elements. We show that a semisimple element in G(k) is real if and only if it is a product of two involutions in ...

Let q be a power of a prime, l a prime not dividing q, d a positive integer coprime to both l and the multiplicative order of q mod l and n a positive integer. A. Watanabe proved that there is a perfect isometry between the principal l−blocks of GLn(q) and GLn(q ) where the correspondence of characters is give by Shintani descent. In the same paper Watanabe also prove that if l and q are odd an...

The relation R̃ on a monoid S provides a natural generalisation of Green’s relation R. If every R̃-class of S contains an idempotent, S is left semiabundant; if R̃ is a left congruence then S satisfies (CL). Regular monoids, indeed left abundant monoids, are left semiabundant and satisfy (CL). However, the class of left semiabundant monoids is much larger, as we illustrate with a number of example...

Let G be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes in G.

We study the effect of Howe correspondence on Harish-Chandra series for type I dual pairs over finite fields with odd characteristic. define a bijection obtained from this correspondence, and enjoying property “having minimal unipotent support”. Finally, we examine interaction between weak cuspidality.

The group generated by unipotent n X n complex matrices is SL„(C), and every member of the latter is a product of three unipotent matrices. The group generated by unipotent operators on Hilbert space Jf is GL(Jf ), and every invertible operator is a product of six unipotent operators of order 2. An operator U on a Hilbert space is called unipotent [3, p. 100] if U = 1 + N, where N is nilpotent....