The q-rook monoid Rn(q) is a semisimple \Bbb C(q)-algebra that specializes when q → 1 to \Bbb C[Rn], where Rn is the monoid of n × n matrices with entries from l0, 1r and at most one nonzero entry in each row and column. We use a Schur-Weyl duality between Rn(q) and the quantum general linear group Uq\euf gl(r) to compute a Frobenius formula, in the ring of symmetric functions, for the irreducible characters of Rn(q). We then derive a recursive Murnaghan-Nakayama rule for these characters, and we use Robinson-Schensted-Knuth insertion to derive a Roichman rule for these characters. We also define a class of standard elements on which it is sufficient to compute characters. The results for Rn(q) specialize when q e 1 to analogous results for Rn.

/pdf/character-formulas-for-q-rook-monoid-algebras-2ixqf7m58q.pdf

Character Formulas for q -Rook Monoid Algebras

In this paper we extend the Robinson-Schensted-Knuth (RSK) superinsertion algorithm to hook-multipartitions and derive the super Frobenius formula for the characters of cyclotomic Hecke algebras (Linear and Multilinear Algebra, DOI: 10.1080/03081087.2019.1663140) via the RSK superinsertion algorithm. In particular, we obtain a new proof of Mitsuhashi's super Frobenius formula for the characters of Iwahori-Hecke algebras.

RSK superinsertion and super Frobenius formulae

In this paper we extend the Robinson-Schensted-Knuth (RSK) superinsertion algorithm to hook-multipartitions and derive the super Frobenius formula for the characters of cyclotomic Hecke algebras via the RSK superinsertion algorithm. As a corollary, we obtain a new proof of Mitsuhashi's super Frobenius formula for the characters of Iwahori-Hecke algebras.

Robinson-Schensted-Knuth Superinsertion and Super Frobenius Formulae

/pdf/robinson-schensted-knuth-insertion-and-characters-of-9bswr80jtr.pdf

Robinson-Schensted-Knuth insertion and characters of cyclotomic Hecke algebras

Authors: Liina Nagirnaja, Alexandra M. Lopes, Wu-Lin Charng, Brian Miller, Rytis Stakaitis, Ieva Golubickaite, Alexandra Stendahl, Tianpengcheng Luan, Corinna Friedrich, Eisa Mahyari, Eloise Fadial, Laura Kasak, Katinka Vigh-Conrad, Manon S. Oud, Miguel J. Xavier, Samuel R. Cheers, Emma R. James, Jingtao Guo, Timothy G Jenkins, Antoni Riera-Escamilla, Alberto Barros, Filipa Carvalho, Susana Fernandes, João Gonçalves, Christina A. Gurnett, Niels Jørgensen, Davor Jezek, Emily S Jungheim, Sabine Kliesch, Robert I. McLachlan, Kenan R Omurtag, Adrian Pilatz, Jay Sandlow, James Smith, Michael L. Eisenberg, James M Hotaling,Keith A. Jarvi, Margus Punab, Ewa Rajpert-De Meyts, Douglas T. Carrell, Csilla Krausz, Maris Laan, Moira K. O’Bryan, Peter N. Schlegel, Frank Tüttelmann, Joris A. Veltman, Kristian Almstrup, Kenneth I. Aston, Donald F. Conrad*

Title: Diverse Monogenic Subforms of Human Spermatogenic Failure

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Robinson-Schensted-Knuth insertion and characters of cyclotomic Hecke algebras

Title: Diverse Monogenic Subforms of Human Spermatogenic Failure