Gröbner-Shirshov Bases for the Cyclotomic Hecke Algebra of Type A

Munayim DILXAT, Abdukadir OBUL, Dong LIU

Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (2) : 309-316.

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Acta Mathematica Sinica, Chinese Series ›› 2023, Vol. 66 ›› Issue (2) : 309-316. DOI: 10.12386/A20210074

Gröbner-Shirshov Bases for the Cyclotomic Hecke Algebra of Type A

  • Munayim DILXAT1, Abdukadir OBUL1, Dong LIU2
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Abstract

In this paper, we discuss the Gröbner--Shirshov bases and a linear bases of the cyclotomic Hecke algebra of type A. First, by computing the compositions, we construct a Gröbner--Shirshov bases of the cyclotomic Hecke algebra of type A. Then using this Gröbner--Shirshov bases and the composition-diamond lemma we give a linear bases of the cyclotomic Hecke algebra of type A.

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Gröbner-Shirshov bases / cyclotomic Hecke algebra of type A / linear basis

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Munayim DILXAT, Abdukadir OBUL, Dong LIU. Gröbner-Shirshov Bases for the Cyclotomic Hecke Algebra of Type A. Acta Mathematica Sinica, Chinese Series, 2023, 66(2): 309-316 https://doi.org/10.12386/A20210074

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