Braching Graph entspricht Young Graph, Folgerungen und Beispiele
Referenzen: Kleshchev S. 12-14, S. 16-17, Okounkov—Vershik S. 15-19
Vortrag 12: Specht Moduln oder der klassische Ansatz
25.01.1017, Nadine
Definitionen: Permutationsmoduln, Specht Modul
Specht Moduln sind irreduziebl
alle irreduziblen Moduln sind Specht Moduln
Untermodultheorem
Permutationsmoduln zerfallen
Referenzen: Sagan S. 60-66
Vortrag 13: Folgerungen von Okounkov—Vershik
01.02.2017, Denise
Young's seminormal form
Young's orthogonal form
Murnaghan--Nakayama rule
Referenzen: Okounkov—Vershik Kapitel 6 und 7, Kleshchev S. 17-20
Literatur
Alperin, J. L. (1-CHI); Bell, Rowen B. (1-CHI) Groups and representations. (English summary)
Graduate Texts in Mathematics, 162. Springer-Verlag, New York, 1995. x+194 pp. $49.95. ISBN 0-387-94525-3
Fulton, William (1-CHI); Harris, Joe [Harris, Joseph Daniel] (1-HRV) Representation theory. A first course. Graduate Texts in Mathematics, 129. Readings in Mathematics.
Springer-Verlag, New York, 1991. xvi+551 pp. $49.50; $29.50 paperbound. ISBN 0-387-97527-6; 0-387-97495-4
Sagan, Bruce E. [Sagan, Bruce Eli] (1-MIS) The symmetric group. Representations, combinatorial algorithms, and symmetric functions. Second edition. Graduate Texts in Mathematics, 203.
Springer-Verlag, New York, 2001. xvi+238 pp. $44.95. ISBN 0-387-95067-2
Lang, Serge (1-YALE) Algebra. (English summary) Revised third edition. Graduate Texts in Mathematics, 211.
Springer-Verlag, New York, 2002. xvi+914 pp. $69.95. ISBN 0-387-95385-X
Kleshchev, Alexander (1-OR) Linear and projective representations of symmetric groups. Cambridge Tracts in Mathematics, 163.
Cambridge University Press, Cambridge, 2005. xiv+277 pp. $80.00. ISBN 0-521-83703-0
Py, P. [Py, Pierre] (F-ENSLY) On representation theory of symmetric groups. (English. Russian summary) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 301 (2003), Teor. Predst. Din. Sist. Komb. i
Algoritm. Metody. 9, 229–242, 245–246; reprinted in J. Math. Sci. (N.Y.) 129 (2005), no. 2, 3806–3813.
Vershik, A. M. [Vershik, Anatoli?i Moiseevich] (RS-AOS2); Okounkov, A. Yu. [Okounkov, Andrei] (1-PRIN) A new approach to representation theory of symmetric groups. II. (Russian. English, Russian summaries) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) 307 (2004), Teor. Predst. Din. Sist. Komb. i
Algoritm. Metody. 10, 57–98, 281; translation in J. Math. Sci. (N. Y.) 131 (2005), no. 2, 5471–5494.
Ceccherini-Silberstein, Tullio [Ceccherini-Silberstein, Tullio G.] (I-SAN); Scarabotti, Fabio (I-ROME); Tolli, Filippo (I-ROME3) Representation theory of the symmetric groups. The Okounkov-Vershik approach, character formulas, and partition algebras. Cambridge Studies in Advanced Mathematics, 121.
Cambridge University Press, Cambridge, 2010. xvi+412 pp. $78.00. ISBN 978-0-521-11817-0
Tânia Silva, Slides Title: Two different approaches to the representation theory of the symmetric group and the rook monoid,
Abstract: There's a long history about the representation theory of the symmetric group and the rook monoid. Since the 19th century many mathematicians contributed to this theories, where the Young diagrams always take an important role. We'll try to resume the classic approach, which uses the Young symmetrizers and the Specht modules, and a more recent one which uses Jucys-Murphy elements and Gelfand-Zetlin bases.
(Conference talk, Young women in Representation theory, Bonn June 23-25 2016)