Geodesic
Cuspidal ribbon tableaux in affine type A
Abbasian, Dina1 ; Difulvio, Lena1 ; Muth, Robert2 ; Pasternak, Gabrielle1 ; Sholtes, Isabella1 ; Sinclair, Frances1
1 Washington & Jefferson College 60 S. Lincoln St. Washington PA 15301 (USA)
2 Duquesne University Department of Mathematics and Computer Science 600 Forbes Ave. Pittsburgh PA 15282 (USA)
Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 285-319

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For any convex preorder on the set of positive roots of affine type A, we classify and construct all associated cuspidal and semicuspidal skew shapes. These combinatorial objects correspond to cuspidal and semicuspidal skew Specht modules for the Khovanov-Lauda-Rouquier algebra of affine type A. Cuspidal skew shapes are ribbons, and we show that every skew shape has a unique ordered tiling by cuspidal ribbons. This tiling data provides an upper bound, in the bilexicographic order on Kostant partitions, for labels of simple factors of Specht modules.

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DOI : 10.5802/alco.260
Classification : 20C08, 20C30, 05E10, 05E16, 17B22, 06A11
Keywords: Young diagrams, ribbon tableaux, Specht modules, Khovanov-Lauda-Rouquier algebras, quiver Hecke algebras

Abbasian, Dina 1 ; Difulvio, Lena 1 ; Muth, Robert 2 ; Pasternak, Gabrielle 1 ; Sholtes, Isabella 1 ; Sinclair, Frances 1

1 Washington & Jefferson College 60 S. Lincoln St. Washington PA 15301 (USA)
2 Duquesne University Department of Mathematics and Computer Science 600 Forbes Ave. Pittsburgh PA 15282 (USA)
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     author = {Abbasian, Dina and Difulvio, Lena and Muth, Robert and Pasternak, Gabrielle and Sholtes, Isabella and Sinclair, Frances},
     title = {Cuspidal ribbon tableaux in affine type {A}},
     journal = {Algebraic Combinatorics},
     pages = {285--319},
     publisher = {The Combinatorics Consortium},
     volume = {6},
     number = {2},
     year = {2023},
     doi = {10.5802/alco.260},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5802/alco.260/}
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%A Pasternak, Gabrielle
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Abbasian, Dina; Difulvio, Lena; Muth, Robert; Pasternak, Gabrielle; Sholtes, Isabella; Sinclair, Frances. Cuspidal ribbon tableaux in affine type A. Algebraic Combinatorics, Tome 6 (2023) no. 2, pp. 285-319. doi: 10.5802/alco.260

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