Answering a question of Geoff Robinson, we compute the large n limiting proportion of iGL(n, q)=q[n2=2], where iGL(n, q) denotes the number of involutions in the group GL(n, q). We give similar results for the finite unitary, symplectic, and orthogonal groups, in both odd and even characteristic. At the heart of this work are certain new "sum = product" identities. Our self-contained treatment of the enumeration of involutions in even characteristic symplectic and orthogonal groups may also be of interest.
Bibliographical noteFunding Information:
Fulman was partially supported by Simons Foundation Grant 400528. Guralnick was partially supported by NSF grants DMS-1302886 and DMS-1600056. Stanton was partially supported by NSF grant DMS-1148634.
© de Gruyter 2017.