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.
- N. Davidson, J. R. Kujawa, R. Muth and J. Zhu, Superalgebra deformations of web categories: finite webs, (2023), 64 pp., (submitted), arXiv
- N. Davidson, J. R. Kujawa and R. Muth, Webs of Type P, (2021), 41pp., (submitted), arXiv
- N. Davidson, J. R. Kujawa and R. Muth, Howe Duality of Type P, (2021), 46 pp. (submitted), arXiv
- T. Einolf, R. Muth and J. Wilkinson, Injectively k-colored rooted forests, (2021), 22pp., (submitted), arXiv
- D. Florentino, E. Moy and R. Muth, Cooperative half-guards in art galleries, (2020), 16 pp., (submitted), arXiv
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- A. Kleshchev and R. Muth, Imaginary Schur-Weyl duality, Memoirs of the American Mathematical Society 245 (2017), no. 1157, xvii, 83 pp., arXiv