Embedding Deligne's category Rep(St) in the Heisenberg category

被引：4

作者：

Likeng, Samuel Nybobe ^{[1
]}

Savage, Alistair ^{[1
]}

机构：

[1] STEM Complex, Dept Math & Stat, 150 Louis Pasteur Pvt, Ottawa, ON K1N 6N5, Canada

来源：

QUANTUM TOPOLOGY | 2021年 / 12卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Categorification; partition category; Deligne category; Heisenberg category; symmetric group; partition algebra; monoidal category; HECKE ALGEBRAS; PRODUCT;

D O I：

10.4171/QT/147

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We define a faithful linear monoidal functor from the partition category, and hence from Deligne's category Rep(S-t), to the additive Karoubi envelope of the Heisenberg category. We show that the induced map on Grothendieck rings is injective and corresponds to the Kronecker coproduct on symmetric functions.

引用

页码：211 / 242

页数：32

共 30 条

[1] Trace as an Alternative Decategorification Functor
Beliakova, Anna
Guliyev, Zaur
Habiro, Kazuo
Lauda, Aaron
[J]. ACTA MATHEMATICA VIETNAMICA, 2014, 39 (04) : 425 - 480
[2] G-colored partition algebras as centralizer algebras of wreath products
Bloss, M
[J]. JOURNAL OF ALGEBRA, 2003, 265 (02) : 690 - 710
[3] Brundan J., 2018, Algebr. Comb., V1, P523
[4] Brundan J., 2018, ARXIV181203255MATHCT
[5] On the definition of quantum Heisenberg category
Brundan, Jonathan
Savage, Alistair
Webster, Ben
[J]. ALGEBRA & NUMBER THEORY, 2020, 14 (02) : 275 - 321
[6] W-ALGEBRAS FROM HEISENBERG CATEGORIES
Cautis, Sabin
Lauda, Aaron D.
Licata, Anthony M.
Sussan, Joshua
[J]. JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 2018, 17 (05) : 981 - 1017
[7] CECCHERINISILBE.T, 2010, OKOUNKOV VERSHIK APP, V121
[8] Jellyfish Partition Categories
Comes, Jonathan
[J]. ALGEBRAS AND REPRESENTATION THEORY, 2020, 23 (02) : 327 - 347
[9] On blocks of Deligne's category Rep(St)
Comes, Jonathan
Ostrik, Victor
[J]. ADVANCES IN MATHEMATICS, 2011, 226 (02) : 1331 - 1377
[10] Deligne P., 2007, Tata Inst. Fund. Res. Studies Math, P209

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