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A Relation for Domino Robinson-Schensted Algorithms
Thomas Pietraho
Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USA
tpietrah@bowdoin.edu
Annals of Combinatorics 13 (4) pp.519-532 December, 2009
AMS Subject Classification: 05E10
Abstract:
We describe a map relating hyperoctahedral Robinson-Schensted algorithms on standard domino tableaux of unequal rank. Iteration of this map relates the algorithms defined by Garfinkle and Stanton-White and when restricted to involutions, this construction answers a question posed by van Leeuwen. The principal technique is derived from operations defined on standard domino tableaux by Garfinkle which must be extended to this more general setting.
Keywords: domino tableaux, Robinson-Schensted algorithm
References:

1. Bonnafé, C., Geck, M., Iancu, L., Lam, T.: On domino insertion and Kazhdan-Lusztig cells in type Bn. Progr. Math. (to appear)

2. Carré, C., Leclerc, B.: Splitting the square of a Schur function into its symmetric and antisymmetric parts. J. Algebraic Combin. 4(3), 201--–231 (1995)

3. Garfinkle, D.: On the classification of primitive ideals for complex classical Lie algebras (I). Compositio Math. 75(2), 135–--169 (1990)

4. Garfinkle, D.: On the classication of primitive ideals for complex classical Lie algebras (II). Compositio Math. 81(3), 307–--336 (1992)

5. Gordon, I.G.: Quiver varieties, Category O for rational Cherednik algebras, and Hecke algebras. Internat. Math. Res. Pap. IMRP 3, rpn006 (2008)

6. Gordon, I.G., Martino, M.: Calogero-Moser space, restricted rational Cherednik algebras and two-sided cells. Math. Res. Lett. 16(2), 255–--262 (2009)

7. van Leeuwen, M.A.A.: The Robinson-Schensted and Schutzenberger algorithms, an elementary approach. Electron. J. Combin. 3(2), #R15 (1996)

8. van Leeuwen, M.A.A.: Edge sequences, ribbon tableaux, and an action of affine permutations. European J. Combin. 20(2), 175--–195 (1999)

9. van Leeuwen, M.A.A.: Some bijective correspondences involving domino tableaux. Electron. J. Combin. 7, #R35 (2000)

10. Lusztig, G.: Hecke algebras with unequal parameters. CRM Monograph Series 18, American Mathematical Society, Providence (2003)

11. Okada, S: Wreath products by the symmetric groups and product posets of Young's lattices. J. Combin. Theory Ser. A 55(1), 14--–32 (1990)

12. Pietraho, T.: Equivalence Classes in the Weyl groups of type Bn. J. Algebraic Combin. 27(2), 247--–262 (2008)

13. Stanton, D.W., White, D.E.: A Schensted algorithm for rim hook tableaux. J. Combin. Theory Ser. A 40(2), 211--–247 (1985)