RUS  ENG
Полная версия
ЖУРНАЛЫ // Moscow Mathematical Journal

Mosc. Math. J., 2021, том 21, номер 3, страницы 507–565 (Mi mmj804)

Deligne categories and the periplectic Lie superalgebra
Inna Entova-Aizenbud, Vera Serganova

References

1. M. Balagovic, Z. Daugherty, I. Entova-Aizenbud, I. Halacheva, J. Hennig, M. S. Im, G. Letzter, E. Norton, V. Serganova, and C. Stroppel, “Translation functors and decomposition numbers for the periplectic Lie superalgebra $\mathfrak{p}(n)$”, Math. Res. Lett., 26:3 (2019), 643–710  crossref  mathscinet  zmath
2. M. Balagović, Z. Daugherty, I. Entova-Aizenbud, I. Halacheva, J. Hennig, M. S. Im, G. Letzter, E. Norton, V. Serganova, and C. Stroppel, “The affine VW supercategory”, Selecta Math. (N.S.), 26:2 (2020), 20, 42 pp.  crossref  mathscinet  zmath
3. B. D. Boe, J. R. Kujawa, and D. K. Nakano, “Complexity and module varieties for classical Lie superalgebras”, Int. Math. Res. Not. IMRN, 2011, no. 3, 696–724  mathscinet  zmath
4. J. Brundan, J. Comes, D. Nash, and A. Reynolds, “A basis theorem for the affine oriented Brauer category and its cyclotomic quotients”, Quantum Topol., 8:1 (2017), 75–112  crossref  mathscinet  zmath
5. J. Brundan and A. P. Ellis, “Monoidal supercategories”, Comm. Math. Phys., 351:3 (2017), 1045–1089  crossref  mathscinet  zmath  adsnasa
6. C. Carmeli and R. Fioresi, “Superdistributions, analytic and algebraic super Harish-Chandra pairs”, Pacific J. Math., 263:1 (2013), 29–51  crossref  mathscinet  zmath
7. C.-W. Chen, “Finite-dimensional representations of periplectic Lie superalgebras”, J. Algebra, 443 (2015), 99–125  crossref  mathscinet  zmath
8. C.-W. Chen and Y.-N. Peng, “Affine periplectic Brauer algebras”, J. Algebra, 501 (2018), 345–372  crossref  mathscinet  zmath
9. E. T. Cline, B. J. Parshall, and L. L. Scott, “Duality in highest weight categories”, Classical groups and related topics (Beijing, 1987), Contemp. Math., 82, Amer. Math. Soc., Providence, RI, 1989, 7–22  crossref  mathscinet
10. K. Coulembier, “The periplectic Brauer algebra”, Proc. Lond. Math. Soc. (3), 117:3 (2018), 441–482  crossref  mathscinet  zmath
11. K. Coulembier, “Tensor ideals, Deligne categories and invariant theory”, Selecta Math. (N.S.), 24:5 (2018), 4659–4710  crossref  mathscinet  zmath
12. K. Coulembier and M. Ehrig, “The periplectic Brauer algebra II: Decomposition multiplicities”, J. Comb. Algebra, 2:1 (2018), 19–46  crossref  mathscinet  zmath
13. K. Coulembier and M. Ehrig, The periplectic Brauer algebra III: the Deligne category, arXiv: 1704.07547 [math.RT]  mathscinet
14. K. Coulembier, I. Entova-Aizenbud, and T. Heidersdorf, Monoidal abelian envelopes and a conjecture of Benson–Etingof, arXiv: 1911.04303 [math.RT]
15. P. Deligne, “Catégories tannakiennes”, The Grothendieck Festschrift, v. II, Progr. Math., 87, Birkhäuser Boston, Boston, MA, 1990, 111–195  mathscinet  zmath
16. P. Deligne, “Catégories tensorielles”, Mosc. Math. J., 2 (2002), 227–248  mathnet  crossref  mathscinet  zmath
17. P. Deligne, “La catégorie des représentations du groupe symétrique $S_t$, lorsque $t$ n'est pas un entier naturel”, Algebraic groups and homogeneous spaces, Tata Inst. Fund. Res. Stud. Math., 19, Tata Inst. Fund. Res., Mumbai, 2007, 209–273  mathscinet  zmath
18. P. Deligne, G. I. Lehrer, and R. B. Zhang, “The first fundamental theorem of invariant theory for the orthosymplectic super group”, Adv. Math., 327 (2018), 4–24  crossref  mathscinet  zmath
19. P. Deligne and J. S. Milne, “Tannakian categories”, Hodge cycles, motives, and Shimura varieties, Lecture Notes in Mathematics, 900, Springer-Verlag, 1982, 101–228  crossref  mathscinet
20. M. Duflo and V. Serganova, On associated variety for Lie superalgebras, arXiv: math/0507198 [math.RT]
21. I. Entova-Aizenbud, V. Hinich, and V. Serganova, “Deligne categories and the limit of categories $\mathrm {Rep}(\mathrm{GL}(m|n))$”, Int. Math. Res. Not. IMRN, 2020, no. 15, 4602–4666  crossref  mathscinet  zmath
22. P. Etingof, “Representation theory in complex rank, II”, Adv. Math., 300 (2016), 473–504  crossref  mathscinet  zmath
23. P. Etingof, S. Gelaki, D. Nikshych, and V. Ostrik, Tensor categories, Mathematical Surveys and Monographs, 205, American Mathematical Society, Providence, RI, 2015  crossref  mathscinet  zmath
24. M. Gorelik, “The center of a simple $P$-type Lie superalgebra”, J. Algebra, 246:1 (2001), 414–428  crossref  mathscinet  zmath
25. J. R. Kujawa and B. C. Tharp, “The marked Brauer category”, J. Lond. Math. Soc. (2), 95:2 (2017), 393–413  crossref  mathscinet  zmath
26. A. Masuoka, “Harish-Chandra pairs for algebraic affine supergroup schemes over an arbitrary field”, Transform. Groups, 17:4 (2012), 1085–1121  crossref  mathscinet  zmath  elib
27. J. S. Milne, Algebraic groups. The theory of group schemes of finite type over a field, Cambridge Studies in Advanced Mathematics, 170, Cambridge University Press, Cambridge, 2017  mathscinet  zmath
28. D. Moon, “Tensor product representations of the Lie superalgebra ${\mathfrak p}(n)$ and their centralizers”, Comm. Algebra, 31:5 (2003), 2095–2140  crossref  mathscinet  zmath
29. R. Nagpal, S. V. Sam, and A. Snowden, “Noetherianity of some degree two twisted skew-commutative algebras”, Selecta Math. (N.S.), 25:1 (2019), 4, 26 pp.  crossref  mathscinet  zmath
30. S. Sahi, H. Salmasian, and V. Serganova, “The Capelli eigenvalue problem for Lie superalgebras”, Math. Z., 294:1-2 (2020), 359–395  crossref  mathscinet  zmath
31. V. Serganova, “On representations of the Lie superalgebra $p(n)$”, J. Algebra, 258:2 (2002), 615–630  crossref  mathscinet  zmath
32. V. Serganova, “On the superdimension of an irreducible representation of a basic classical Lie superalgebra”, Supersymmetry in mathematics and physics, Lecture Notes in Math., 2027, Springer, Heidelberg, 2011, 253–273  crossref  mathscinet  zmath
33. V. Serganova, “Classical Lie superalgebras at infinity”, Advances in Lie superalgebras, Springer INdAM Ser., 7, Springer, Cham, 2014, 181–201  crossref  mathscinet  zmath  elib
34. B. C. Tharp, Representations of the marked Brauer algebra, Ph.D. thesis, University of Oklahoma Graduate College, 2017  mathscinet


© МИАН, 2026