%% This BibTeX bibliography file was created using BibDesk. %% http://bibdesk.sourceforge.net/ %% Created for Nicholas Beaton at 2020-02-05 10:13:09 +1100 %% Saved with string encoding Unicode (UTF-8) @comment{jabref-meta: databaseType:bibtex;} @misc{Stanley2006, Author = {Stanley, R. P.}, Date-Modified = {2019-04-17 21:30:01 +1000}, Eprint = {math/0606467}, Eprinttype = {arXiv}, Title = {A conjectured combinatorial interpretation of the normalized irreducible character values of the symmetric group}, Year = {2006}} @article{Stanley2003/04, Author = {Stanley, R. P.}, Date-Modified = {2019-04-17 21:31:54 +1000}, Journal = {S\'{e}m. Lothar. Combin.}, Pages = {Art. B50d, 11 pages}, Title = {Irreducible symmetric group characters of rectangular shape}, Url = {https://www.mat.univie.ac.at/~slc/wpapers/s50stanley.html}, Volume = {50}, Year = {2004}, Bdsk-Url-1 = {https://www.mat.univie.ac.at/~slc/wpapers/s50stanley.html}} @article{Nazarov1990, Author = {Nazarov, M. L.}, Date-Modified = {2019-04-17 20:12:41 +1000}, Doi = {10.1112/jlms/s2-42.3.437}, Journal = {J. London Math. Soc. (2)}, Number = {3}, Pages = {437--451}, Title = {Young's orthogonal form of irreducible projective representations of the symmetric group}, Volume = {42}, Year = {1990}, Bdsk-Url-1 = {https://doi.org/10.1112/jlms/s2-42.3.437}} @misc{SpinAlgebraic2018, Author = {Matsumoto, S. and {\'S}niady, P.}, Date-Modified = {2020-02-05 10:08:49 +1100}, Eprint = {1811.10434}, Eprinttype = {arXiv}, Note = {To appear in {\em Alg. Combin.}}, Title = {Linear versus spin: representation theory of the symmetric groups}, Year = {2020}} @article{Kerov1994, Author = {Kerov, S. and Olshanski, G.}, Date-Modified = {2019-04-17 20:08:11 +1000}, Journal = {C. R. Acad. Sci. Paris S\'er. I Math.}, Number = {2}, Pages = {121--126}, Title = {Polynomial functions on the set of {Y}oung diagrams}, Volume = {319}, Year = {1994}} @article{Schur1911, Author = {Schur, J.}, Date-Modified = {2019-04-17 20:13:17 +1000}, Doi = {10.1515/crll.1911.139.155}, Journal = {J. Reine Angew. Math.}, Pages = {155--250}, Title = {{\"U}ber die {D}arstellung der symmetrischen und der alternierenden {G}ruppe durch gebrochene lineare {S}ubstitutionen}, Volume = {139}, Year = {1911}, Bdsk-Url-1 = {https://doi.org/10.1515/crll.1911.139.155}} @book{Stanley1999, Address = {Cambridge}, Author = {Stanley, R. P.}, Date-Modified = {2019-04-18 15:58:03 +1000}, Doi = {10.1017/CBO9780511609589}, Number = {62}, Publisher = {Cambridge University Press}, Series = {Cambridge Studies in Advanced Mathematics}, Title = {Enumerative Combinatorics, {V}ol. 2}, Year = {1999}, Bdsk-Url-1 = {https://doi.org/10.1017/CBO9780511609589}} @book{Macdonald1995, Address = {New York}, Author = {Macdonald, I. G.}, Date-Modified = {2019-04-17 20:09:23 +1000}, Edition = {2}, Publisher = {The Clarendon Press, Oxford University Press}, Series = {Oxford Mathematical Monographs}, Title = {Symmetric Functions and {H}all Polynomials}, Year = {1995}} @article{Matsumoto2018, Author = {Matsumoto, S.}, Date-Modified = {2019-04-17 20:10:50 +1000}, Doi = {10.3842/SIGMA.2018.053}, Journal = {SIGMA Symmetry Integrability Geom. Methods Appl.}, Pages = {Paper No. 053, 13 pages}, Title = {A spin analogue of {K}erov polynomials}, Volume = {14}, Year = {2018}, Bdsk-Url-1 = {https://doi.org/10.3842/SIGMA.2018.053}} @misc{DeStavolaThesis, Author = {De Stavola, D.}, Date-Modified = {2019-04-17 20:04:24 +1000}, Eprint = {1805.04065}, Eprinttype = {arXiv}, School = {Universit{\"a}t Z{\"u}rich}, Title = {Asymptotic results for Representation Theory}, Year = {2017}, Bdsk-Url-1 = {https://arxiv.org/abs/1805.04065v1}} @article{Do_ga_2010, Author = {M. Do{\l}{\k{e}}ga and V. F{\'{e}}ray and P. {\'{S}}niady}, Date-Modified = {2019-04-17 20:05:33 +1000}, Doi = {10.1016/j.aim.2010.02.011}, Journal = {Adv. Math.}, Number = {1}, Pages = {81--120}, Title = {Explicit combinatorial interpretation of Kerov character polynomials as numbers of permutation factorizations}, Volume = {225}, Year = 2010, Bdsk-Url-1 = {https://doi.org/10.1016%2Fj.aim.2010.02.011}, Bdsk-Url-2 = {https://doi.org/10.1016/j.aim.2010.02.011}} @misc{Dousse2017, Author = {J. Dousse and V. F{\'e}ray}, Date-Modified = {2019-04-17 20:06:04 +1000}, Eprint = {1710.05652}, Eprinttype = {arXiv}, Title = {Asymptotics for skew standard {Y}oung tableaux via bounds for characters}, Year = {2017}} @article{FeraySniady2011a, Author = {F{\'e}ray, V. and {\'S}niady, P.}, Date-Modified = {2019-04-17 20:07:05 +1000}, Doi = {10.4007/annals.2011.173.2.6}, Journal = {Ann. of Math. (2)}, Number = {2}, Pages = {887--906}, Title = {{Asymptotics of characters of symmetric groups related to {S}tanley character formula}}, Volume = {173}, Year = {2011}, Bdsk-Url-1 = {http://dx.doi.org/10.4007/annals.2011.173.2.6}} @article{Matsumoto2018a, Author = {Matsumoto, S. and {\'S}niady, P.}, Date-Modified = {2020-02-05 10:13:01 +1100}, Doi = {10.1007/s00029-020-0535-2}, Journal = {Sel. Math. New Ser.}, Number = {1}, Pages = {Art. 10, 59 pages}, Title = {Random strict partitions and random shifted tableaux}, Volume = {26}, Year = {2020}} @article{Ivanov2004, Abstract = {In 1993, S. Kerov obtained a central limit theorem for the Plancherel measure on Young diagrams. The Plancherel measure is a natural probability measure on the set of irreducible characters of the symmetric group Sn. Kerov's theorem states that, as n{\textrightarrow}∞, the values of irreducible characters at simple cycles, appropriately normalized and considered as random variables, are asymptotically independent and converge to Gaussian random variables. In the present work we obtain an analog of this theorem for projective representations of the symmetric group. Bibliography: 27 titles.}, Author = {Ivanov, V. N.}, Date-Modified = {2019-04-17 20:07:37 +1000}, Doi = {10.1023/B:JOTH.0000024615.07311.fe}, Journal = {J. Math. Sci.}, Number = {3}, Pages = {2330--2344}, Title = {Gaussian Limit for Projective Characters of Large Symmetric Groups}, Volume = {121}, Year = {2004}, Bdsk-Url-1 = {https://doi.org/10.1023/B:JOTH.0000024615.07311.fe}}