Hook-content Formulae for Symplectic and Orthogonal Tableaux

نویسندگان

  • PETER S. CAMPBELL
  • ANNA STOKKE
چکیده

By considering the specialisation sλ(1, q, q , . . . , q) of the Schur function, Stanley was able to describe a formula for the number of semistandard Young tableaux of shape λ in terms of two properties of the boxes in the diagram for λ. Using specialisations of symplectic and orthogonal Schur functions, we derive corresponding formulae, first given by El Samra and King, for the number of semistandard symplectic and orthogonal λ-tableaux.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Lattice Path Proofs for Determinantal Formulas for Symplectic and Orthogonal Characters

We give bijective proofs for Jacobi{Trudi-type and Giambelli-type identities for symplectic and orthogonal characters. These proofs base on interpreting King and El-Sharkaway's symplectic tableaux, Proctor's odd and intermediate symplectic tableaux, Proctor's and King and Welsh's orthogonal tableaux, and Sundaram's odd orthogonal tableaux in terms of certain families of nonintersecting lattice ...

متن کامل

A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

متن کامل

Pieri Rules for Classical Groups and Equinumeration between Generalized Oscillating Tableaux and Semistandard Tableaux

We present several equinumerous results between generalized oscillating tableaux and semistandard tableaux and give a representation-theoretic proof to them. As one of the key ingredients of the proof, we provide Pieri rules for the symplectic and orthogonal groups.

متن کامل

Determinantal Forms for Symplectic and Orthogonal Schur Functions

Symplectic and orthogonal Schur functions can be defined combinatorially in a manner similar to the classical Schur functions. This paper demonstrates that they can also be expressed as determinants. These determinants are generated using planar decompositions of tableaux into strips and the equivalence of these determinants to symplectic or orthogonal Schur functions is established by Gessel-V...

متن کامل

Jeu-de-taquin promotion and a cyclic sieving phenomenon for semistandard hook tableaux

Jeu-de-taquin promotion yields a bijection on the set of semistandard λ-tableaux with entries bounded by k. In this note, we determine the order of jeu-de-taquin promotion on the set of semistandard hook tableaux CST ((n−m, 1m), k), with entries bounded by k, and on the set of semistandard hook tableaux with fixed content α, CST ((n−m, 1m), k, α). We give a bijection between CST ((n−m, 1m), k, ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2007