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QUASI-SPLIT SYMMETRIC PAIRS OF $U(\mathfrak {gl}_N)$ AND THEIR SCHUR ALGEBRAS

Published online by Cambridge University Press:  21 September 2020

YIQIANG LI  and
JIERU ZHU
YIQIANG LI
Affiliation:
Department of Mathematics, University at Buffalo, SUNY Buffalo, NY 14260, USAyiqiang@buffalo.edu
JIERU ZHU*
Affiliation:
Department of Mathematics, University at Buffalo, SUNY Buffalo, NY 14260, USA
*
jieruzhu@buffalo.edu
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Abstract

We establish explicit isomorphisms of two seemingly-different algebras, and their Schur algebras, arising from the centralizers of two different type B Weyl group actions in Schur-like dualities. We provide a presentation of the geometric counterpart of the above Schur algebras in [1] specialized at $q=1$ .

Type
Article
Information
Nagoya Mathematical Journal , Volume 245 , March 2022 , pp. 1 - 27
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Copyright
© (2020) The Authors. The publishing rights in this article are licenced to Foundation Nagoya Mathematical Journal under an exclusive license

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References

Bao, H., Kujawa, J., Li, Y., and Wang, W., Geometric Schur duality of classical type , Transform. Groups 23 (2018), no. 2, 329–389.10.1007/s00031-017-9447-4CrossRefGoogle Scholar
Bao, H. and Wang, W., Canonical bases arising from quantum symmetric pairs , Invent. Math. 213 (2018), no. 3, 1099–1177.10.1007/s00222-018-0801-5CrossRefGoogle Scholar
Bao, H. and Wang, W., A new approach to Kazhdan-Lusztig theory of type B via quantum symmetric pairs , Astérisque 402 (2018), no. 402, vii+134.Google Scholar
Beilinson, A., Lusztig, G., and MacPherson, R., A geometric setting for the quantum deformation of GLn, Duke Math. J. 61 (1990), 655–677.10.1215/S0012-7094-90-06124-1CrossRefGoogle Scholar
Doty, S. and Giaquinto, A., Presenting Schur algebras , Int. Math. Res. Not. 38 (2002), no. 36, 1907–1944.10.1155/S1073792802201026CrossRefGoogle Scholar
Green, R., Hyperoctahedral Schur algebras , J. Algebra 192 (1997), no. 1, 418–438.10.1006/jabr.1996.6935CrossRefGoogle Scholar
Hu, J. and Stoll, F., On double centralizer properties between quantum groups and Ariki-Koike algebras , J. Algebra 275 (2004), no. 1, 397–418.10.1016/j.jalgebra.2003.10.026CrossRefGoogle Scholar
Kolb, S., Quantum symmetric Kac-Moody pairs , Adv. Math. 267 (2014), 395–469.10.1016/j.aim.2014.08.010CrossRefGoogle Scholar
Lai, C.-J., Nakano, D., and Xiang, Z., On q-Schur algebras corresponding to Hecke algebras of type B, arXiv e-prints (2019), arXiv:1902.07682.Google Scholar
Letzter, G., Subalgebras which appear in quantum Iwasawa decompositions , Canad. J. Math. 49 (1997), no. 6, 1206–1223.10.4153/CJM-1997-059-4CrossRefGoogle Scholar
Li, Y., On canonical bases for the Letzter algebra Ui(sl2), J. Pure Appl. Algebra 224 (2020), 106227.10.1016/j.jpaa.2019.106227CrossRefGoogle Scholar
Li, Y. and Wang, W., Positivity vs negativity of canonical bases , Bull. Inst. Math. Acad. Sin. (N.S.) 13 (2018), no. 2, 143–198.Google Scholar
Mazorchuk, V. and Stroppel, C., G(l,k,d)-modules via groupoids , J. Algebraic Combin. 43 (2016), no. 1, 11–32.10.1007/s10801-015-0623-0CrossRefGoogle Scholar
Sakamoto, M. and Shoji, T., Schur–Weyl reciprocity for Ariki-Koike algebras , J. Algebra 221 (1999), no. 1, 293–314.10.1006/jabr.1999.7973CrossRefGoogle Scholar
Springer, T. A., The classification of involutions of simple algebraic groups , J. Fac. Sci. Univ. Tokyo Sect. IA Math. 34 (1987), 655–670.Google Scholar