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).

Lattices Generated by Two Orbits of Subspaces under Finite Singular Symplectic Groups

In the paper titled “Lattices generated by two orbits of subspaces under finite classical group” by Wang and Guo. The subspaces in the lattices are characterized and the geometricity is classified. In this paper, the result above is generalized to singular symplectic space. This paper characterizes the subspaces in these lattices, classifies their geometricity, and computes their characteristic polynomials.

MINIMAL IRREDUCIBILITY AND THE UNIPOTENT CHARACTERS OF GROUPS OF TYPE Bm AND Cm

In this paper we prove that the (non-trivial) irreducible complex unipotent characters of a finite classical group G of type Bm or Cm in odd characteristic are reducible over any proper subgroup of G, apart from very few notable exceptions.