Low-Dimensional Complex Characters of the Symplectic and Orthogonal Groups

The Ore conjecture

“…Arguing as above for (22), replacing 3/4 in (23) by 19/20, we see that |E(x)| < 1 if |C G (x)| is less than 2 34 if q = 2, less than 3 38 if q = 3, and less than q 39 if q = 4. Assume |C G (x)| is greater than these bounds.…”

“…First we collect some results from [38] on complex irreducible characters of relatively small degrees for orthogonal groups.…”

Complex representation growth of finite quasisimple groups of Lie type

“…Instead, we will use partial results obtained by Tiep and Zalesskii [18], Nguyen [17] and Guralnick and Tiep [6]. These results give us some of the Lusztig polynomials corresponding to the smallest representation degrees.…”

“…(A description of how these lists were produced is given in [13].) On the other hand, P. Tiep and A. Zalesskii [18] have found the polynomials giving the few smallest character 851 degrees of classical groups, regardless of rank, and this list has been extended by Guralnick and Tiep [6] and H. N. Nguyen [17] for the symplectic and orthogonal groups.…”

Conjugacy classes of small sizes in the linear and unitary groups

“…The results obtained have proved very useful in various applications. The irreducible complex characters of finite Lie-type groups of small degrees were studied in [12,16] and more recently in [15]. In these papers, the irreducible complex characters of degrees up to a certain bound are classified and it is proved that there is a large gap between the degrees of these characters and the next degree.…”