A NOTE ON SYMMETRIC LINEAR FORMS AND TRACES ON THE RESTRICTED QUANTUM GROUP Ūq(sl(2))

Faitg, Matthieu 大阪大学 DOI:10.18910/76674

2020.07

概要

In this paper we prove two results about SLF(Ūq), the algebra of symmetric linear forms on the restricted quantum group Ūq = Ūq (sl(2)). First, we express any trace on finite dimensional projective Ūq-modules as a linear combination in the basis of SLF(Ūq) constructed by Gainutdinov - Tipunin and also by Arike. In particular, this allows us to determine the symmetric linear form corresponding to the modified trace on projective Ūq-modules. Second, we give the explicit multiplication rules between symmetric linear forms in this basis.

論文の公開元へ

参考文献

[1] Y. Arike: A construction of symmetric linear functions on the restricted quantum group U¯ q(sl(2)), Osaka J. Math. 47 (2010), 535–557.

[2] A. Beliakova, C. Blanchet and A.M. Gainutdinov: Modified trace is a symmetrised integral, arXiv:1801.00321.

[3] A. Beliakova, C. Blanchet and N. Geer: Logarithmic Hennings invariants for restricted quantum sl(2), Algebr. Geom. Topol. 18 (2018), 4329–4358.

[4] C. Curtis and I. Reiner: Representation Theory of Finite Groups and Associative Algebras, Interscience Publishers, 1962.

[5] M. Faitg: Modular group representations in combinatorial quantization with non-semisimple Hopf alge- bras, arXiv:1805.00924.

[6] B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov and I.Yu. Tipunin: Modular group representations and fusion in logarithmic conformal field theories and in the quantum group center, Commun. Math. Phys. 265 (2006), 47–93.

[7] B.L. Feigin, A.M. Gainutdinov, A.M. Semikhatov and I.Yu. Tipunin: Kazhdan-Lusztig correspondence for the representation category of the triplet W-algebra in logarithmic CFT, Theoret. Mat. Phys. 148 (2006), 1210–1235.

[8] N. Geer, J. Kujawa and B. Patureau-Mirand: Generalized trace and modified dimension functions on ribbon categories, Selecta Math. (N.S.) 17 (2011), 453–504.

[9] A.M. Gainutdinov and I.Yu. Tipunin: Radford, Drinfeld and Cardy boundary states in the (1, p) logarithmic conformal field models, J. Phys. A 42 (2009), 315207, 30pp.

[10] E. Ibanez: Evaluable Jones-Wenzl idempotents at root of unity and modular representation on the center of U¯ q sl(2), PhD Thesis (in French), arXiv:1604.03681.

[11] C. Kassel: Quantum Groups, Graduate Texts in Mathematics 155, Springer-Verlag, 1995.

[12] H. Kondo and Y. Saito: Indecomposable decomposition of tensor products of modules over the restricted quantum enveloping algebra associated to sl2, J. Algebra 330 (2011), 103–129.

[13] J. Murakami: Generalized Kashaev invariants for knots in three manifolds, Quantum Topol. 8, (2017), 35–73.

[14] D.E. Radford: The trace function and Hopf algebras, J. Algebra 163 (1994), 583–622.

[15] R. Suter: Modules over U¯ q(sl(2)), Commu. Math. Phys. 163 (1994), 359–393.

参考文献をもっと見る

分野

大学

学位論文種類・取得年

言語

A NOTE ON SYMMETRIC LINEAR FORMS AND TRACES ON THE RESTRICTED QUANTUM GROUP Ūq(sl(2))

概要

関連論文

ON THE VALUES OF UNIPOTENT CHARACTERS OF FINITE CHEVALLEY GROUPS OF TYPE E_7 IN CHARACTERISTIC 2

TORSION FUNCTION ON CHARACTER VARIETIES

On branching laws of Speh representations

NUMERICAL INVARIANTS AND MODULI SPACES FOR LINE ARRANGEMENTS

On plectic and p-adic Hodge theory (本文)

参考文献

分野

大学

学位論文種類・取得年

言語

コピーが完了しました

URLをコピーしました

A NOTE ON SYMMETRIC LINEAR FORMS AND TRACES ON THE RESTRICTED QUANTUM GROUP Ūq(sl(2))

概要

関連論文

ON THE VALUES OF UNIPOTENT CHARACTERS OF FINITE CHEVALLEY GROUPS OF TYPE E_7 IN CHARACTERISTIC 2

TORSION FUNCTION ON CHARACTER VARIETIES

On branching laws of Speh representations

NUMERICAL INVARIANTS AND MODULI SPACES FOR LINE ARRANGEMENTS

On plectic and p-adic Hodge theory (本文)

参考文献