Research

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My research interests include representation theory and algebraic combinatorics, with a focus on the following topics:

  • Representation theory of symmetric groups and Lie algebras.
  • Tableau combinatorics and canonical bases for quantum groups.
  • Categorification and diagrammatic algebra.

Preprints:

  1. N. Davidson, J. R. Kujawa, R. Muth and J. Zhu, Superalgebra deformations of web categories: finite webs, (2023), 64 pp., (submitted), arXiv
  2. N. Davidson, J. R. Kujawa and R. Muth, Webs of Type P, (2021), 41pp., (submitted), arXiv
  3. N. Davidson, J. R. Kujawa and R. Muth, Howe Duality of Type P, (2021), 46 pp. (submitted), arXiv
  4. T. Einolf, R. Muth and J. Wilkinson, Injectively k-colored rooted forests, (2021), 22pp., (submitted), arXiv
  5. D. Florentino, E. Moy and R. Muth, Cooperative half-guards in art galleries, (2020), 16 pp., (submitted), arXiv

Papers:

  1. D. Abbasian, L. Difulvio, R. Muth, G. Pasternak, I. Sholtes and F. Sinclair, Cuspidal ribbon tableaux in affine type A, Algebraic Combinatorics, 37 pp., (to appear), arXiv
  2. D. Denniston, R. Muth and V. Singh, The configuration space of a robotic arm over a graph, Discrete Mathematics, Algorithms and Applications, 20pp. (to appear), arXiv
  3. A. Kleshchev and R. Muth, Schurifying quasi-hereditary algebras, Proceedings of the London Mathematical Society 125 (2022), 54pp., https://doi.org/10.1112/plms.12466, arXiv
  4. R. Muth, L. Speyer and L. Sutton, Decomposable Specht modules indexed by bihooks II, Algebras and Representation Theory 26 (2021), 40pp., https://doi.org/10.1007/s10468-021-10093-3, arXiv
  5. A. Iams, H. Johnston and R. Muth, Searching for quicksand ideals in partially ordered sets, Australasian Journal of Combinatorics 79(2) (2021), 27 pp., https://ajc.maths.uq.edu.au/pdf/79/ajc_v79_p256.pdf, arXiv
  6. A. Kleshchev and R. Muth, Based quasi-hereditary algebras, Journal of Algebra 558 (2020), 18 pp., https://doi.org/10.1016/j.jalgebra.2019.04.034, arXiv
  7. A. Kleshchev and R. Muth, Generalized Schur algebras, Algebra & Number Theory 14 (2020), 44 pp., https://doi.org/10.2140/ant.2020.14.501, arXiv
  8. R. Muth, Super RSK correspondence with symmetry, Electronic Journal of Combinatorics 26(2) (2019), #P2.27, 26 pp., https://doi.org/10.37236/8150, arXiv
  9. A. Kleshchev and R. Muth, Affine zigzag algebras and imaginary strata for KLR algebras, Transactions of the American Mathematical Society 371 (2019), 44 pp., https://doi.org/10.1090/tran/7464, arXiv
  10. R. Muth, Graded skew Specht modules and cuspidal modules for Khovanov-Lauda-Rouquier algebras of affine type A, Algebras and Representation Theory 22 (2018), 32 pp., https://doi.org/10.1007/s10468-018-9808-2, arXiv
  11. A. Kleshchev and R. Muth, Stratifying KLR algebras of affine ADE types, Journal of Algebra 475 (2017), 37 pp., https://doi.org/10.1016/j.jalgebra.2016.07.006, arXiv
  12. A. Kleshchev and R. Muth, Imaginary Schur-Weyl duality, Memoirs of the American Mathematical Society 245 (2017), no. 1157, xvii, 83 pp., arXiv