Canonical Brauer induction and symmetric groups

Robert Boltje; Burkhard Külshammer

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 2, page 453-460
  • ISSN: 0392-4041

Abstract

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Imitating the approach of canonical induction formulas we derive a formula that expresses every character of the symmetric group as an integer linear combination of Young characters. It is different from the well-known formula that uses the determinantal form.

How to cite

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Boltje, Robert, and Külshammer, Burkhard. "Canonical Brauer induction and symmetric groups." Bollettino dell'Unione Matematica Italiana 8-B.2 (2005): 453-460. <http://eudml.org/doc/196034>.

@article{Boltje2005,
abstract = {Imitating the approach of canonical induction formulas we derive a formula that expresses every character of the symmetric group as an integer linear combination of Young characters. It is different from the well-known formula that uses the determinantal form.},
author = {Boltje, Robert, Külshammer, Burkhard},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {symmetric groups; partitions; Möbius function; Young subgroups; irreducible characters; Young characters; determinantal form; Solomon formula; alternating character; groups of virtual characters; generalized characters},
language = {eng},
month = {6},
number = {2},
pages = {453-460},
publisher = {Unione Matematica Italiana},
title = {Canonical Brauer induction and symmetric groups},
url = {http://eudml.org/doc/196034},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Boltje, Robert
AU - Külshammer, Burkhard
TI - Canonical Brauer induction and symmetric groups
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/6//
PB - Unione Matematica Italiana
VL - 8-B
IS - 2
SP - 453
EP - 460
AB - Imitating the approach of canonical induction formulas we derive a formula that expresses every character of the symmetric group as an integer linear combination of Young characters. It is different from the well-known formula that uses the determinantal form.
LA - eng
KW - symmetric groups; partitions; Möbius function; Young subgroups; irreducible characters; Young characters; determinantal form; Solomon formula; alternating character; groups of virtual characters; generalized characters
UR - http://eudml.org/doc/196034
ER -

References

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  1. BOLTJE, R., A general theory of canonical induction formulae, J. Alg., 206 (1998), 293-343. Zbl0913.20001MR1637292
  2. BLEY, W. - BOLTJE, R., Cohomological Mackey functors in number theory, Preprint 2001. Zbl1061.11059MR2032439
  3. CURTIS, C.W. - REINER, I., Methods of representation theory, Vol. II, John Wiley & Sons (New York, 1987). Zbl0616.20001MR892316
  4. JAMES, G. - KERBER, A., The representation theory of the symmetric group, Addison-Wesley (Reading, 1981). Zbl0491.20010MR644144
  5. SPIEGEL, E. - O'DONELL, C.J., Incidence algebras, Marcel Dekker (New York, 1997). Zbl0871.16001MR1445562

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