This was a reading seminar organized by Alexander Caviedes, Cesar Ceballos, Peter Crooks and Iva Halacheva. We followed Fulton's book "Young-Tableaux".
Location: Fields Institute
Tuesdays 11:00am. Fall 2013
Wednesdays 2:00pm. Winter 2014
Fridays 11:00 am. Summer 2014
Schedule 2013-2014
September 24
Cesar Ceballos
Bumping and Sliding : Operations on Young Tableaux. Schensted-bumping operation. Schutzerberg-sliding algorithm. [F, Int, Ch1]
October 1
Alexander Caviedes
Words and Elementary transformations: Words. Knuth Transformations. Schur Polynomials. [F, Sect 2.1, 2.2] Alex' Notes
October 8
Alexander Caviedes
Schur Polynomials: Schur Polynomials. Pieri's Formula. Kostka Numbers. [F, Sect 2.2] Alex' Notes
October 15
Iva Halacheva
Robinson-Schensted-Knuth Correspondence I: RSK correspondence. [F, Sect 4.1]
October 22
Iva Halacheva
Robinson-Schensted-Knuth Correspondence II: Applications of the RSK correspondence. Symmetry Theorem. Matrix Ball construction. [F, Sect 4.2, 4.3]
October 29
Cesar Ceballos
The Littlewood-Richardson Rule: Yamanouchi word. Littlewood-Richardson Tableaux. Littlewood-Richardson Rule. [F, Ch 5]
November 5
Alexander Caviedes
Symmetric Polynomials: Complete, Elementary, Monomial, Newton and Schur symmetric Polynomials. Jacobi-Trudi Formula. The ring of symmetric functions. [F, Ch 6] Alex' Notes
November 12
Peter Crooks
The action of the symmetric group on tableaux. Specht Modules I. [F, Sect 7.1, 7.2]
November 19
Peter Crooks
Representations of the symmetric group. Specht Modules II. Irreducible representations of the symmetric group. [F, Sect 7.1, 7.2] Peter's Notes
November 26
Iva Halacheva
The ring of representations and symmetric functions I. [F, Sect 7.3]
December 10
Iva Halacheva
The ring of representations and symmetric functions II. [F, Sect 7.3]
January 13*
Alexander Caviedes
Schur Modules. [F, Sect 8.1 ]
January 22
Alexander Caviedes, Peter Crooks, Iva Halacheva
Exercise Section I: Hook length formula [F, Sect 4.3, 7.3]. Character of Mlambda [F, Sect 7.2]. Consequences of Litlewood-Richardson's rule [F, Chapter 5]
January 29
Alexander Caviedes
Schur Modules II, Irreducible representations of GLm(C)
February 5
Cesar Ceballos, Peter Crooks, Iva Halacheva
Exercise Section II
February 12
Peter Crooks
Gl(E) representations from Sn representations I. Weyl functor [F, Sect 8.1, 8.2]
February 23
Peter Crooks
Gl(E) representations from Sn representations II. Character of Elambda [F, Sect 8.3, 8.4]
March 7*
Iva Halacheva
Plucker embeddings I. Projective embeddings of flag varieties [F, Sect 9.1]
March 12
Iva Halacheva
Plucker embeddings II. Projective embedding of flag varieties [F, Sect 9.1]
March 19
Iva Halacheva
Plucker embeddings III. Homogeneous coordinate ring of the flag variety. Geometric Invariant theory [F, Sect 9.1, 9.2]
March 26
Peter Crooks
Representations of Gl(E) and line bundles I. [F, Sect 9.3]
April 2
Peter Crooks
Representations of Gl(E) and line bundles II [F, Sect 9.3]
April 9
Peter Crooks
Representations of Gl(E) and line bundles III [F, Sect 9.3]
April 16
Cesar Ceballos
Schubert Calculus on Grassmannians. Schubert cells and varieties. Duality Theorem [F, Sect 9.4]
April 30
Cesar Ceballos
Schubert Calculus on Grassmannians. Schubert cells and varieties. Pieri's Formula [F, Sect 9.4] Cesar's Notes
May 7
Alexander Caviedes
Fixed points of torus actions. Schubert cells in flag manifolds [F, Sect 10.1, 10.2]
May 14
Alexander Caviedes
Schubert varieties. Dual Schubert cells and dual Schubert varieties in flag manifolds. Duality Theorem [F, Sect 10.2]
July 11
Alexander Caviedes
Chern Classes of line bundles. Leray Hirsch Theorem [F, Sect 10.2, Appendix B1]
July 18
Alexander Caviedes
Cohomology ring of flag manifolds [F, Sect 10.2, Appendix B1]
July 25
Peter Crooks
Relations among Schubert varieties I [F, Sect 10.3]
August 1*
Peter Crooks
Relations among Schubert varieties II [F, Sect 10.3]
August 8
Peter Crooks
Relations among Schubert varieties III [F, Sect 10.3]
August 8
Cesar Ceballos
Schubert Polynomials [F, Sect 10.4]
August 15
Cesar Ceballos
Bruhat Order [F, Sect 10.5]
August 15
Iva Halacheva
Applications to the Grassmannian [F, Sect 10.6]
Bibliography
[F] Young-Tableaux. William Fulton.