Bar weights of bar partitions and spin character zeros
Christine Bessenrodt
Leibniz Universität Hannover Institut für Algebra, Zahlentheorie und Diskrete Mathematik, Fakultät für Mathematik und Physik Welfengarten 1 D-30167 Hannover Germany
DOI: 10.1007/s10801-006-0050-3
Abstract
The main combinatorial result in this article is a classification of bar partitions of n which are of maximal p-bar weight for all odd primes p \leq n. As a consequence, we show that apart from very few exceptions any irreducible spin character of the double covers of the symmetric and alternating groups vanishes on some element of odd prime order.
Pages: 107–124
Keywords: keywords bar partitions; bar cores; bar weights; symmetric group; alternating group; spin characters; character zeros
Full Text: PDF
References
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6. D. Hanson, “On a theorem of Sylvester and Schur,” Canad. Math. Bull. 16 (1973), 195-199.
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8. G. James and A. Kerber, “The representation theory of the symmetric group,” Encyclopedia of Mathematics and its Applications 16, Addison-Wesley (1981).
9. G. Malle, G. Navarro, and J.B. Olsson, “Zeros of characters of finite groups,” J. Group Theory 3 (2000), 353-368.
10. A.O. Morris, “The spin representation of the symmetric group,” Canad. J. Math. 17 (1965), 543-549.
11. A.O. Morris and A.K. Yaseen, “Some combinatorial results involving Young diagrams,” Math. Proc. Camb. Phil. Soc. 99 (1986), 23-31.
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2. C. Bessenrodt, G. Malle, and J.B. Olsson, “Separating characters by blocks,” J. London Math. Soc. 73(2) (2006), 493-505.
3. C. Bessenrodt and J.B. Olsson, “The 2-blocks of the covering groups of the symmetric groups,” Advances in Math. 129 (1997), 261-300.
4. C. Bessenrodt and J.B. Olsson, “Prime power degree representations of the double covers of the symmetric and alternating groups,” J. London Math. Soc. 66(2) (2002), 313-324.
5. C. Bessenrodt and J.B. Olsson, “Weights of partitions and character zeros,” Electron. J. Comb. 11(2) (2004), R5.
6. D. Hanson, “On a theorem of Sylvester and Schur,” Canad. Math. Bull. 16 (1973), 195-199.
7. P.N. Hoffman and J.F. Humphreys, Projective Representations of the Symmetric Groups, Clarendon Press Oxford, 1992.
8. G. James and A. Kerber, “The representation theory of the symmetric group,” Encyclopedia of Mathematics and its Applications 16, Addison-Wesley (1981).
9. G. Malle, G. Navarro, and J.B. Olsson, “Zeros of characters of finite groups,” J. Group Theory 3 (2000), 353-368.
10. A.O. Morris, “The spin representation of the symmetric group,” Canad. J. Math. 17 (1965), 543-549.
11. A.O. Morris and A.K. Yaseen, “Some combinatorial results involving Young diagrams,” Math. Proc. Camb. Phil. Soc. 99 (1986), 23-31.
12. J.B. Olsson, “Combinatorics and representations of finite groups,” Vorlesungen aus dem FB Mathematik der Univ. Essen, Heft 20 (1993).
13. I. Schur, “Einige S\ddot atze \ddot uber Primzahlen mit Anwendungen auf Irreduzibilit\ddot atsfragen. I,” Sitzungsberichte der Preuss. Akad. d. Wiss. 1929, Phys.-Math. Klasse, pp. 125-136.