Group representations and lattices
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- by Benedict H. Gross
- J. Amer. Math. Soc. 3 (1990), 929-960
- DOI: https://doi.org/10.1090/S0894-0347-1990-1071117-8
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References
- Allan Adler, Some integral representations of $\textrm {PSL}_{2}(\textbf {F}_{p})$ and their applications, J. Algebra 72 (1981), no. 1, 115â145. MR 634619, DOI 10.1016/0021-8693(81)90314-8
- N. Bourbaki, ĂlĂ©ments de mathĂ©matique. Fasc. XXXVIII: Groupes et algĂšbres de Lie. Chapitre VII: Sous-algĂšbres de Cartan, Ă©lĂ©ments rĂ©guliers. Chapitre VIII: AlgĂšbres de Lie semi-simples dĂ©ployĂ©es, ActualitĂ©s Scientifiques et Industrielles [Current Scientific and Industrial Topics], No. 1364, Hermann, Paris, 1975 (French). MR 0453824
- Michel BrouĂ© and Michel Enguehard, Une famille infinie de formes quadratiques entiĂšres; leurs groupes dâautomorphismes, Ann. Sci. Ăcole Norm. Sup. (4) 6 (1973), 17â51 (French). MR 335654
- Roger W. Carter, Finite groups of Lie type, Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1985. Conjugacy classes and complex characters; A Wiley-Interscience Publication. MR 794307
- J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219
- J. H. Conway and N. J. A. Sloane, Sphere packings, lattices and groups, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 290, Springer-Verlag, New York, 1988. With contributions by E. Bannai, J. Leech, S. P. Norton, A. M. Odlyzko, R. A. Parker, L. Queen and B. B. Venkov. MR 920369, DOI 10.1007/978-1-4757-2016-7 M. Eichler, Ăber die Klassenzahl total definiter quaternionenalgebren, Math. Z. 43 (1937), 102-109. N. Elkies, Letters to N. J. Sloane, 15 August 1989, 15 September 1989.
- Walter Feit, The computations of some Schur indices, Israel J. Math. 46 (1983), no. 4, 274â300. MR 730344, DOI 10.1007/BF02762888
- Walter Feit, The representation theory of finite groups, North-Holland Mathematical Library, vol. 25, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 661045
- Paul GĂ©rardin, Weil representations associated to finite fields, J. Algebra 46 (1977), no. 1, 54â101. MR 460477, DOI 10.1016/0021-8693(77)90394-5
- R. Gow, Schur indices of some groups of Lie type, J. Algebra 42 (1976), no. 1, 102â120. MR 466330, DOI 10.1016/0021-8693(76)90029-6
- R. Gow, On the Schur indices of characters of finite classical groups, J. London Math. Soc. (2) 24 (1981), no. 1, 135â147. MR 623680, DOI 10.1112/jlms/s2-24.1.135
- Robert L. Griess Jr., Automorphisms of extra special groups and nonvanishing degree $2$ cohomology, Pacific J. Math. 48 (1973), 403â422. MR 476878 E. Hecke, Ăber ein fundamentalproblem aus der theorie der Elliptischen modulfunktionen, Abh. Math. Sem. Univ. Hamburg 6 (1928), 235-257 (= Werke 28).
- Ryoshi Hotta and Kiyoshi Matsui, On a lemma of Tate-Thompson, Hiroshima Math. J. 8 (1978), no. 2, 255â268. MR 486178
- J. E. Humphreys, Representations of $\textrm {SL}(2,p)$, Amer. Math. Monthly 82 (1975), 21â39. MR 364478, DOI 10.2307/2319129
- Gregory Karpilovsky, The Schur multiplier, London Mathematical Society Monographs. New Series, vol. 2, The Clarendon Press, Oxford University Press, New York, 1987. MR 1200015
- Vicente Landazuri and Gary M. Seitz, On the minimal degrees of projective representations of the finite Chevalley groups, J. Algebra 32 (1974), 418â443. MR 360852, DOI 10.1016/0021-8693(74)90150-1
- G. Lusztig, Coxeter orbits and eigenspaces of Frobenius, Invent. Math. 38 (1976/77), no. 2, 101â159. MR 453885, DOI 10.1007/BF01408569
- Barry Mazur, Arithmetic on curves, Bull. Amer. Math. Soc. (N.S.) 14 (1986), no. 2, 207â259. MR 828821, DOI 10.1090/S0273-0979-1986-15430-3
- J. S. Milne, The Tate-Ć afareviÄ group of a constant abelian variety, Invent. Math. 6 (1968), 91â105. MR 244264, DOI 10.1007/BF01389836
- John Milnor and Dale Husemoller, Symmetric bilinear forms, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 73, Springer-Verlag, New York-Heidelberg, 1973. MR 0506372
- Daniel Quillen, The $\textrm {mod}$ $2$ cohomology rings of extra-special $2$-groups and the spinor groups, Math. Ann. 194 (1971), 197â212. MR 290401, DOI 10.1007/BF01350050
- Bruno Schoeneberg, Elliptic modular functions: an introduction, Die Grundlehren der mathematischen Wissenschaften, Band 203, Springer-Verlag, New York-Heidelberg, 1974. Translated from the German by J. R. Smart and E. A. Schwandt. MR 0412107
- J.-P. Serre, Complex multiplication, Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965) Thompson, Washington, D.C., 1967, pp. 292â296. MR 0244199
- J.-P. Serre, A course in arithmetic, Graduate Texts in Mathematics, No. 7, Springer-Verlag, New York-Heidelberg, 1973. Translated from the French. MR 0344216
- Jean-Pierre Serre, Linear representations of finite groups, Graduate Texts in Mathematics, Vol. 42, Springer-Verlag, New York-Heidelberg, 1977. Translated from the second French edition by Leonard L. Scott. MR 0450380
- Tetsuji Shioda, Mordell-Weil lattices and Galois representation. I, Proc. Japan Acad. Ser. A Math. Sci. 65 (1989), no. 7, 268â271. MR 1030197 â, Mordell-Weil lattices and sphere packings, preprint, 1989.
- Robert Steinberg, Lectures on Chevalley groups, Yale University, New Haven, Conn., 1968. Notes prepared by John Faulkner and Robert Wilson. MR 0466335
- Robert Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33â56. MR 155937
- John Tate, Endomorphisms of abelian varieties over finite fields, Invent. Math. 2 (1966), 134â144. MR 206004, DOI 10.1007/BF01404549 â, On the conjecture of Birch and Swinnerton-Dyer and a geometric analog, SĂ©m. Bourbaki 306 1965-1966. J. G. Thompson, A simple subgroup of ${E_8}(3)$, Finite Groups (N. Iwahori, ed.), Tokyo, 1976, pp. 113-116.
- J. G. Thompson, Finite groups and even lattices, J. Algebra 38 (1976), no. 2, 523â524. MR 399257, DOI 10.1016/0021-8693(76)90234-9
- Marie-France VignĂ©ras, ArithmĂ©tique des algĂšbres de quaternions, Lecture Notes in Mathematics, vol. 800, Springer, Berlin, 1980 (French). MR 580949 G. van der Geer and M. van der Vlugt, Reed-Muller codes and supersingular curves, Ann. Ăcole. Norm. Sup. (to appear).
- A. E. ZalesskiÄ and I. D. Suprunenko, Representations of dimension $(p^n\pm 1)/2$ of the symplectic group of degree $2n$ over a field of characteristic $p$, VestsÄ« Akad. Navuk BSSR Ser. FÄ«z.-Mat. Navuk 6 (1987), 9â15, 123 (Russian, with English summary). MR 934193
Bibliographic Information
- © Copyright 1990 American Mathematical Society
- Journal: J. Amer. Math. Soc. 3 (1990), 929-960
- MSC: Primary 11H55; Secondary 11H06, 20C10
- DOI: https://doi.org/10.1090/S0894-0347-1990-1071117-8
- MathSciNet review: 1071117