caa a22 4500 386382875 CHVBK 20180307112048.0 cr unu---uuuuu 161130s1989 xx s 000 0 eng 10.1017/S0308210500023933 doi S0308210500023933 pii (NATIONALLICENCE)cambridge-10.1017/S0308210500023933 Poincaré series for the occurrence of certain modular representations of GL(n,p) in the symmetric algebra [Elektronische Daten] The number of occurrences of the Steinberg representation St of GL(n, p) as a composition factor in the symmetric algebra Fp[x1, ... xn] has been determined by several authors. We extend this result to the representations of GL(n, p) which are the closest neighbours of St in the SL(n, p) weight diagram. The method is to play off duality for GL(n, p)-modules against connectivity for M(n, p)-modules. The result is equivalent to determining the cohomology groups of the corresponding indecomposable stable summands of the localisation of an n-fold product of complex projective spaces at the prime p. Copyright © Royal Society of Edinburgh 1989 Carlisle David P. Computer Science Department and University of Manchester, Oxford Road, Manchester M13 9PL, U.K. Walker Grant Mathematics Department, University of Manchester, Oxford Road, Manchester M13 9PL, U.K. Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 27-41 0308-2105 113:1-2<27 1989 113 PRM https://doi.org/10.1017/S0308210500023933 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0308210500023933 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Carlisle David P. Computer Science Department and University of Manchester, Oxford Road, Manchester M13 9PL, U.K NATIONALLICENCE 700 1- Walker Grant Mathematics Department, University of Manchester, Oxford Road, Manchester M13 9PL, U.K NATIONALLICENCE 773 0- Proceedings of the Royal Society of Edinburgh: Section A Mathematics Royal Society of Edinburgh Scotland Foundation 113/1-2(1989), 27-41 0308-2105 113:1-2<27 1989 113 PRM CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge