On the first Cartan invariant of the groupSp(4,p n )

• DOI: 10.1007/bf02560309
• Publication Date: 2007-02-08T05:29:13Z
• Authors: Ye Jiachen
• Keywords: 0101 mathematics; 01 natural sciences

The purpose of this paper is to obtain a formula for computing the first Cartan invariantC 11 (n) of the groupSp(4,p n ). The main results are as follows: Theorem A. If p≥7, then $$\dim R(n,\theta ) = (32^m - r^m - s^m + 1)p^{4m} $$ where r, s are the roots of x 2 −24x+64. Theorem B. If p>7, then $$c_{11}^{(m)} = \left[ {R(n,\theta ):M(n,\theta )} \right]_{k\Gamma _m } = a^m + b^m + c^m + d^m + e^m + f^m + g^m - 2\left( {\alpha ^m + \beta ^m + \gamma ^m } \right)$$ where a, b, c, d are the roots of x 4 −64x 3+804x 2 −2672x+2048; e, f, g. are the roots of x 3 −36x 2 +256x−512; α, β, γ are the roots of x 3 −43x 2 +312x−512.