바로가기메뉴

본문 바로가기 주메뉴 바로가기

logo

  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

Article Contents

Prev Next
e-Submission

Vol.22 No.3

Citation Share

JACOBI-TRUDI TYPE FORMULA FOR PARABOLICALLY SEMISTANDARD TABLEAUX

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2015, v.22 no.3, pp.245-261
https://doi.org/10.7468/jksmeb.2015.22.3.245
KIM, JEE-HYE
KIM,, J. (2015). JACOBI-TRUDI TYPE FORMULA FOR PARABOLICALLY SEMISTANDARD TABLEAUX. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 22(3), 245-261, https://doi.org/10.7468/jksmeb.2015.22.3.245

Abstract

The notion of a parabolically semistandard tableau is a generalisation of Young tableau, which explains combinatorial aspect of various Howe dualities of type A. We prove a Jacobi-Trudi type formula for the character of parabolically semistandard tableaux of a given generalised partition shape by using non-intersecting lattice paths.

keywords
Schur function, Jacobi-Trudi formula, Howe duality, Young tableaux

Reference

1.

Kwon, J.-H.;Park, E.-Y.;. (2015). Duality on Fock spaces and combinatorial energy functions. J. Combin. Theory Ser. A, 134, 121-146. 10.1016/j.jcta.2015.03.005.

2.

Macdonald, I.G.;. Symmetric functions and Hall polynomials.

3.

Stanley, R.P.;. Enumerative Combinatorics.

4.

Cheng, S.-J.;Wang, W.;. (2003). Lie subalgebras of differential operators on the super circle. Publ. Res. Inst. Math. Sci., 39, 545-600. 10.2977/prims/1145476079.

5.

Cheng, S.-J.;Wang, W.;. (2012). Dualities and Representations of Lie Superalgebras. Graduate Studies in Mathematics, 144.

6.

Frenkel, I.B.;. (1985). Representations of Kac-Moody algebras and dual resonance models in Applications of group theory in physics and mathematical physics. Lectures in Appl. Math., 21, 325-353.

7.

Fulton, W.;. Young tableaux, with Application to Representation theory and Geometry.

8.

Gessel, I.;Viennot, G.;. (1985). Binomial determinants, paths, and hook length formulae. Adv. Math., 58, 300-321. 10.1016/0001-8708(85)90121-5.

9.

Howe, R.;. (1989). Remarks on classical invariant theory. Trans. Amer. Math. Soc., 313, 539-570. 10.1090/S0002-9947-1989-0986027-X.

10.

Kac, V.G.;. Infinite-dimensional Lie algebras.

11.

Kac, V.G.;Radul, A.;. (1996). Representation theory of the vertex algebra W1+∞. Transform. Groups, 1, 41-70. 10.1007/BF02587735.

12.

Kashiwara, M.;Vergne, M.;. (1978). On the Segal-Shale-Weil representations and harmonic polynomials. Invent. Math., 44, 1-47. 10.1007/BF01389900.

13.

Kwon, J.-H.;. (2008). Rational semistandard tableaux and character formula for the Lie superalgebra <inline-graphic></inline-graphic>. Adv. Math., 217, 713-739. 10.1016/j.aim.2007.09.001.

14.

Kwon, J.-H.;. (2008). A combinatorial proof of a Weyl type formula for hook Schur polynomials. J. Algber. Comb., 28, 439-459. 10.1007/s10801-007-0109-9.

15.

Cheng, S.-J.;Lam, N.;. (2003). Infinite-dimensional Lie superalgebras and hook Schur functions. Comm. Math. Phys., 238, 95-118. 10.1007/s00220-003-0819-3.

16.

Cheng, S.-J.;Lam, N.;Zhang, R.B.;. (2004). Character formula for infinite-dimensional unitarizable modules of the general linear superalgebra. J. Algebra, 273, 780-805. 10.1016/S0021-8693(03)00538-6.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

e-Submission OA Policy