On characters of Chevalley groups vanishing at the non-semisimple elements

Let [Formula: see text] be a finite simple group of Lie type. In this paper, we study characters of [Formula: see text] that vanish at the non-semisimple elements and whose degree is equal to the order of a maximal unipotent subgroup of [Formula: see text]. Such characters can be viewed as a natural generalization of the Steinberg character. For groups [Formula: see text] of small rank we also determine the characters of this degree vanishing only at the non-identity unipotent elements.

On the Steinberg character of an orthogonal group over a finite field

We determine the irreducible constituents of the Steinberg character of an orthogonal group over a finite field restricted to the orthogonal group of one less dimension.

The Steinberg Character of Finite Classical Groups

Let G be a finite classical group of characteristic p. In this paper, we give an arithmetic criterion of the primes r ≠ p, for which the Steinberg character lies in the principal r-block of G. The arithmetic criterion is obtained from some combinatorial objects (the so-called partition and symbol).

Principal Blocks and the Steinberg Character

We determine the finite simple groups of Lie type of characteristic p, for which the Steinberg character lies in the principal ℓ-block for every prime ℓ ≠ p dividing the order of the group.