@article {MR1163745, AUTHOR = {Boltje, Robert and Snaith, Victor and Symonds, Peter}, TITLE = {Algebraicisation of explicit {B}rauer induction}, JOURNAL = {J. Algebra}, FJOURNAL = {Journal of Algebra}, VOLUME = {148}, YEAR = {1992}, NUMBER = {2}, PAGES = {504--527}, ISSN = {0021-8693,1090-266X}, MRCLASS = {20C15}, MRNUMBER = {1163745}, MRREVIEWER = {Thomas\ R.\ Wolf}, DOI = {10.1016/0021-8693(92)90204-Y}, URL = {https://doi.org/10.1016/0021-8693(92)90204-Y}, } @article {MR0020105, AUTHOR = {Brauer, Richard}, TITLE = {On {A}rtin's {$L$}-series with general group characters}, JOURNAL = {Ann. of Math. (2)}, FJOURNAL = {Annals of Mathematics. Second Series}, VOLUME = {48}, YEAR = {1947}, PAGES = {502--514}, ISSN = {0003-486X}, MRCLASS = {10.0X}, MRNUMBER = {20105}, MRREVIEWER = {M.\ Krasner}, DOI = {10.2307/1969183}, URL = {https://doi.org/10.2307/1969183}, } @article {MR3056296, AUTHOR = {Heide, Gerhard and Saxl, Jan and Tiep, Pham Huu and Zalesski, Alexandre E.}, TITLE = {Conjugacy action, induced representations and the {S}teinberg square for simple groups of {L}ie type}, JOURNAL = {Proc. Lond. Math. Soc. (3)}, FJOURNAL = {Proceedings of the London Mathematical Society. Third Series}, VOLUME = {106}, YEAR = {2013}, NUMBER = {4}, PAGES = {908--930}, ISSN = {0024-6115,1460-244X}, MRCLASS = {20D06 (20C33)}, MRNUMBER = {3056296}, MRREVIEWER = {Hung\ Ngoc\ Nguyen}, DOI = {10.1112/plms/pds062}, URL = {https://doi.org/10.1112/plms/pds062}, } @article {MR1867283, AUTHOR = {Kra\'{s}kiewicz, Witold and Weyman, Jerzy}, TITLE = {Algebra of coinvariants and the action of a {C}oxeter element}, JOURNAL = {Bayreuth. Math. Schr.}, FJOURNAL = {Bayreuther Mathematische Schriften}, NUMBER = {63}, YEAR = {2001}, PAGES = {265--284}, ISSN = {0172-1062}, MRCLASS = {20C30 (05E10 17B01)}, MRNUMBER = {1867283}, MRREVIEWER = {Christine\ Bessenrodt}, } @article {MR3069563, AUTHOR = {Artin, E.}, TITLE = {Zur theorie der l-reihen mit allgemeinen gruppencharakteren}, JOURNAL = {Abh. Math. Sem. Univ. Hamburg}, FJOURNAL = {Abhandlungen aus dem Mathematischen Seminar der Universit\"{a}t Hamburg}, VOLUME = {8}, YEAR = {1931}, NUMBER = {1}, PAGES = {292--306}, ISSN = {0025-5858,1865-8784}, MRCLASS = {99-04}, MRNUMBER = {3069563}, DOI = {10.1007/BF02941010}, URL = {https://doi.org/10.1007/BF02941010}, } @misc{p2023existence, title={On the Existence of Elementwise Invariant Vectors in Representations of Symmetric Groups}, author={Amrutha P and Amritanshu Prasad and Velmurugan S}, year=2023, eprint={2308.08146}, archivePrefix={arXiv}, primaryClass={math.RT} } @incollection {MR2279239, AUTHOR = {Heide, G. and Zalesski, A. E.}, TITLE = {Passman's problem on adjoint representations}, BOOKTITLE = {Groups, rings and algebras}, SERIES = {Contemp. Math.}, VOLUME = 420, PAGES = {163--176}, PUBLISHER = {Amer. Math. Soc., Providence, RI}, YEAR = 2006, ISBN = {978-0-8218-3904-1; 0-8218-3904-7}, MRCLASS = {20C34 (20C05 20C33)}, MRNUMBER = 2279239, MRREVIEWER = {Roderick\ Gow}, DOI = {10.1090/conm/420/07975}, URL = {https://doi.org/10.1090/conm/420/07975}, } @article {MR4328100, AUTHOR = {Yang, Nanying and Staroletov, Alexey M.}, TITLE = {The minimal polynomials of powers of cycles in the ordinary representations of symmetric and alternating groups}, JOURNAL = {J. Algebra Appl.}, FJOURNAL = {Journal of Algebra and its Applications}, VOLUME = {20}, YEAR = {2021}, NUMBER = {11}, PAGES = {Paper No. 2150209, 18}, ISSN = {0219-4988,1793-6829}, MRCLASS = {20C30}, MRNUMBER = {4328100}, MRREVIEWER = {Alejandro\ Pi\~{n}era-Nicolas}, DOI = {10.1142/S0219498821502091}, URL = {https://doi.org/10.1142/S0219498821502091}, } @Article{zbMATH07612832, Author = {Prasad, Dipendra and Raghunathan, Ravi}, Title = {Relations between cusp forms sharing {Hecke} eigenvalues}, FJournal = {Representation Theory}, Journal = {Represent. Theory}, ISSN = {1088-4165}, Volume = {26}, Pages = {1063--1079}, Year = {2022}, Language = {English}, DOI = {10.1090/ert/626}, Keywords = {11F70,22E55}, zbMATH = {7612832}, Zbl = {1512.11052} } @manual{sagemath, Key = {SageMath}, Author = {{The Sage Developers}}, Title = {{S}ageMath, the {S}age {M}athematics {S}oftware {S}ystem ({V}ersion 10.0)}, note = {{\newline \tt https://www.sagemath.org}}, Year = {2023}, } @article {MR3805649, AUTHOR = {Sundaram, Sheila}, TITLE = {On conjugacy classes of {$S_n$} containing all irreducibles}, JOURNAL = {Israel J. Math.}, FJOURNAL = {Israel Journal of Mathematics}, VOLUME = {225}, YEAR = {2018}, NUMBER = {1}, PAGES = {321--342}, ISSN = {0021-2172,1565-8511}, MRCLASS = {05E10 (05E05)}, MRNUMBER = {3805649}, MRREVIEWER = {Zhicong\ Lin}, DOI = {10.1007/s11856-018-1659-3}, URL = {https://doi.org/10.1007/s11856-018-1659-3}, } @article {MR3855421, AUTHOR = {Sundaram, Sheila}, TITLE = {The conjugacy action of {$S_n$} and modules induced from centralisers}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {48}, YEAR = {2018}, NUMBER = {2}, PAGES = {179--225}, ISSN = {0925-9899}, MRCLASS = {20C05 (05E18 06A07 20C15 20C30)}, MRNUMBER = {3855421}, MRREVIEWER = {Stuart Martin}, DOI = {10.1007/s10801-017-0796-9}, URL = {https://doi.org/10.1007/s10801-017-0796-9}, } @article {swanson, AUTHOR = {Swanson, Joshua P.}, TITLE = {On the existence of tableaux with given modular major index}, JOURNAL = {Algebr. Comb.}, FJOURNAL = {Algebraic Combinatorics}, VOLUME = {1}, YEAR = {2018}, NUMBER = {1}, PAGES = {3--21}, MRCLASS = {05E10 (05A20)}, MRNUMBER = {3857157}, MRREVIEWER = {Elizabeth M. Niese}, DOI = {10.5802/alco.4}, URL = {https://doi.org/10.5802/alco.4}, } @article {JAM, AUTHOR = {J\"{o}llenbeck, Armin and Schocker, Manfred}, TITLE = {Cyclic characters of symmetric groups}, JOURNAL = {J. Algebraic Combin.}, FJOURNAL = {Journal of Algebraic Combinatorics. An International Journal}, VOLUME = {12}, YEAR = {2000}, NUMBER = {2}, PAGES = {155--161}, ISSN = {0925-9899}, MRCLASS = {05E15}, MRNUMBER = {1801229}, DOI = {10.1023/A:1026592027019}, URL = {https://doi.org/10.1023/A:1026592027019}, } @book {MR3287258, AUTHOR = {Prasad, Amritanshu}, TITLE = {Representation theory}, SERIES = {Cambridge Studies in Advanced Mathematics}, VOLUME = {147}, NOTE = {A combinatorial viewpoint}, PUBLISHER = {Cambridge University Press, Delhi}, YEAR = {2015}, PAGES = {xii+191}, ISBN = {978-1-107-08205-2}, MRCLASS = {20C30 (05E05 05E10 20G05)}, MRNUMBER = {3287258}, MRREVIEWER = {Bhama Srinivasan}, DOI = {10.1017/CBO9781139976824}, URL = {https://doi.org/10.1017/CBO9781139976824}, } @book {MR3443860, AUTHOR = {Macdonald, I. G.}, TITLE = {Symmetric functions and {H}all polynomials}, SERIES = {Oxford Classic Texts in the Physical Sciences}, EDITION = {Second}, PUBLISHER = {Oxford University Press}, YEAR = 2015, PAGES = {xii+475}, ISBN = {978-0-19-873912-8}, MRCLASS = {05E05 (01A75 05-02 20C30 20C33 20K01 33C80 33D80)}, MRNUMBER = 3443860, }