q - al g / 97 09 01 0 v 2 15 S ep 1 99 7 DOMINO TABLEAUX , SCH
نویسنده
چکیده
We deene an action of the symmetric group S n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight 0 does not depend on the permutation of the weight 0. A bijective proof of the well-known result due to J. Stembridge that the number of self{evacuating tableaux of a given shape and weight = (1 ; : : : ; n+1 2 ] ; n 2 ] ; : : : ; 1), is equal to that of domino tableaux of the same shape and weight 0 = (1 ; : : : ; n+1 2 ]) is given. 0. Introduction Domino tableaux play a signiicant role in the representation theory of the symmetric group S n , and the theory of symmetric polynomials. The shortest deenition of semi-standard domino tableaux is given in 10], p. 139. In particular, the generating function of the number of domino tableaux of shape = (1 2 n 0), and weight 0 = (1 ; : : : ; n+1 2 ]) is given by specializing the Schur polynomial s (x) at x 7 ! y where where the sign depends only on. Recently they were studied in connection with the representation theory of GL n. In particular, in 12] John Stembridge proved the following conjecture by Richard Stanley (who stated it for 0 = (1; 1; : : : ; 1), that is, for standard tableaux).
منابع مشابه
ar X iv : q - a lg / 9 70 90 10 v 1 4 S ep 1 99 7 August 7 , 1997 DOMINO TABLEAUX , SCHÜTZENBERGER INVOLUTION , AND THE SYMMETRIC GROUP ACTION
We define an action of the symmetric group S[ n 2 ] on the set of domino tableaux, and prove that the number of domino tableaux of weight β does not depend on the permutation of the weight β. A bijective proof of the well-known result due to J. Stembridge that the number of self–evacuating tableaux of a given shape and weight β = (β1, . . . , β[ n+1 2 ], β[ n2 ], . . . , β1), is equal to that o...
متن کاملar X iv : h ep - t h / 97 09 01 6 v 1 2 S ep 1 99 7 Free boson representation of DY h̄ ( gl N ) k
متن کامل
ar X iv : q ua nt - p h / 97 09 04 2 v 1 18 S ep 1 99 7 Measurement and state preparation via ion trap quantum computing
We investigate in detail the effects of a QND vibrational number measurement made on single ions in a recently proposed measurement scheme for the vibrational state of a register of ions in a linear rf trap [C. D'Helon and G. The performance of a measurement shows some interesting patterns which are closely related to searching.
متن کاملar X iv : h ep - e x / 97 11 01 6 v 1 2 1 N ov 1 99 7 Results on Λ 0 Production at HERMES
The production of Λ 0 's at the HERMES experiment is presented. Prospects for the future of Λ measurements at HERMES are discussed.
متن کاملX iv : h ep - p h / 97 09 22 2 v 1 2 S ep 1 99 7 Few - body aspects of non - perturbative QCD
After some general remarks on non-perturbative QCD I present shortly models which lead to a color-electric flux tube formation. The implications of such a flux tube formation especially on high energy scattering are discussed.
متن کاملذخیره 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 1997