Affine oriented Frobenius Brauer categories

References

• Brundan, J., Comes, J., Kujawa, J. R. (2019). A basis theorem for the degenerate affine oriented Brauer-Clifford supercategory. Can. J. Math. 71(5):1061–1101. arXiv:1706.09999, DOI: 10.4153/cjm-2018-030-8..
   Web of Science ®Google Scholar
• Brundan, J., Comes, J., Nash, D., Reynolds, A. (2017). A basis theorem for the affine oriented Brauer category and its cyclotomic quotients. Quantum Topol. 8(1):75–112. arXiv:1404.6574, DOI: 10.4171/QT/87..
   Web of Science ®Google Scholar
• Brundan, J., Ellis, A. P. (2017). Monoidal supercategories. Commun. Math. Phys. 351(3):1045–1089. arXiv:1603.05928, DOI: 10.1007/s00220-017-2850-9..
   Web of Science ®Google Scholar
• Berele, A., Regev, A. (1987). Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras. Adv. Math. 64(2):118–175. DOI: 10.1016/0001-8708(87)90007-7.
   Web of Science ®Google Scholar
• Brundan, J. (2018). On the definition of Heisenberg category. Algebraic Comb. 1(4):523–544. arXiv:1709.06589, DOI: 10.5802/alco.26..
   Google Scholar
• Brundan, J., Stroppel, C. (2012). Gradings on walled Brauer algebras and Khovanov’s arc algebra. Adv. Math. 231(2):709–773. arXiv:1107.0999, DOI: 10.1016/j.aim.2012.05.016..
   Web of Science ®Google Scholar
• Brundan, J., Savage, A., Webster, B. (2021). Foundations of Frobenius Heisenberg categories. J. Algebra 578:115–185. arXiv:2007.01642, DOI: 10.1016/j.jalgebra.2021.02.025..
   Web of Science ®Google Scholar
• Brundan, J., Savage, A., Webster, B. (2022). Quantum Frobenius Heisenberg categorification. J. Pure Appl. Algebra 226(1):106792, 50. arXiv:2009.06690, DOI: 10.1016/j.jpaa.2021.106792..
   Web of Science ®Google Scholar
• Comes, J., Wilson, B. (2012). Deligne’s category Rep¯(GLδ) and representations of general linear supergroups. Represent. Theory 16:568–609. arXiv:1108.0652, DOI: 10.1090/S1088-4165-2012-00425-3.
   Google Scholar
• Deligne, P. (2007). La catégorie des représentations du groupe symétrique St, lorsque t n’est pas un entier naturel. In: Algebraic Groups and Homogeneous Spaces, volume 19 of Tata Institute of Fundamental Research in Mathematics. Mumbai: Tata Institute of Fundamental Research, pp. 209–273.
   Google Scholar
• Ehrig, M., Stroppel, C. (2016). Schur-Weyl duality for the Brauer algebra and the ortho-symplectic Lie superalgebra. Math. Z. 284(1–2):595–613. arXiv:1412.7853, DOI: 10.1007/s00209-016-1669-y..
   Web of Science ®Google Scholar
• Gao, M., Rui, H., Song, L., Su, Y. (2019). Affine walled Brauer-Clifford superalgebras. J. Algebra 525:191–233. arXiv:1708.05135, DOI: 10.1016/j.jalgebra.2019.01.014..
   Web of Science ®Google Scholar
• Jung, J. H., Kang, S.-J. (2014). Mixed Schur-Weyl-Sergeev duality for queer Lie superalgebras. J. Algebra 399:516–545. arXiv:1208.5139, DOI: 10.1016/j.jalgebra.2013.08.029..
   Web of Science ®Google Scholar
• Khovanov, M. (2014). Heisenberg algebra and a graphical calculus. Fund. Math. 225(1):169–210. arXiv:1009.3295, DOI: 10.4064/fm225-1-8..
   Google Scholar
• Koike, K. (1989). On the decomposition of tensor products of the representations of the classical groups: by means of the universal characters. Adv. Math. 74(1):57–86. DOI: 10.1016/0001-8708(89)90004-2..
   Web of Science ®Google Scholar
• Lee Shader, C., Moon, D. (2002). Mixed tensor representations and rational representations for the general linear Lie superalgebras. Commun. Algebra 30(2):839–857. DOI: 10.1081/AGB-120013185..
   Web of Science ®Google Scholar
• Mackaay, M., Savage, A. (2018). Degenerate cyclotomic Hecke algebras and higher level Heisenberg categorification. J. Algebra 505:150–193. arXiv:1705.03066, DOI: 10.1016/j.jalgebra.2018.03.004..
   Web of Science ®Google Scholar
• Rui, H., Su, Y. (2015). Affine walled Brauer algebras and super Schur-Weyl duality. Adv. Math. 285:28–71. arXiv:1305.0450, DOI: 10.1016/j.aim.2015.07.018..
   Web of Science ®Google Scholar
• Rosso, D., Savage, A. (2017). A general approach to Heisenberg categorification via wreath product algebras. Math. Z. 286(1–2):603–655. arXiv:1507.06298, DOI: 10.1007/s00209-016-1776-9..
   Web of Science ®Google Scholar
• Sartori, A. (2014). The degenerate affine walled Brauer algebra. J. Algebra 417:198–233. arXiv:1305.2347, DOI: 10.1016/j.jalgebra.2014.06.030..
   Web of Science ®Google Scholar
• Savage, A. (2019). Frobenius Heisenberg categorification. Algebraic Comb. 2(5):937–967. arXiv:1802.01626, DOI: 10.5802/alco.73..
   Google Scholar
• Savage, A. (2020). Affine wreath product algebras. Int. Math. Res. Not. IMRN 10:2977–3041. arXiv:1709.02998, DOI: 10.1093/imrn/rny092..
   Google Scholar
• Savage, A. (2021). String diagrams and categorification. In: Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification, volume 337 of Progress in Mathematics. Cham: Birkhäuser/Springer. arXiv:1806.06873, DOI: 10.1007/978-3-030-63849-8.
   Google Scholar
• Sergeev, A. N. (1984). Representations of the Lie superalgebras 𝔤𝔩(n,m) and Q(n) in a space of tensors. Funktsional. Anal. i Prilozhen. 18(1):80–81.
   Google Scholar
• Sergeev, A. N. (1984). Tensor algebra of the identity representation as a module over the Lie superalgebras Gl(n, m) and Q(n). Mat. Sb. (N.S.) 123(165)(3):422–430.
   Google Scholar
• Turaev, V. G. (1989). Operator invariants of tangles, and R-matrices. Izv. Akad. Nauk SSSR Ser. Mat. 53(5):1073–1107, 1135. DOI: 10.1070/IM1990v035n02ABEH000711..
   Google Scholar
• Turaev, V., Virelizier, A. (2017). Monoidal Categories and Topological Field Theory, volume 322 of Progress in Mathematics. Cham: Birkhäuser/Springer. DOI: 10.1007/978-3-319-49834-8.
   Google Scholar