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<p>Let <i>F</i> be a field of characteristic 0 and let <i>E</i> be the infinite-dimensional Grassmann algebra over <i>F</i>. In the first part of this paper we give an algorithm calculating the generating function of the cocharacter sequence of the <i>n</i> × <i>n</i> upper triangular matrix algebra <i>UT</i><sub><i>n</i></sub>(<i>E</i>) with entries in <i>E</i>, lying in a strip of a fixed size. In the second part we compute the double Hilbert series <i>H</i>(<i>E</i>; T<sub><i>k</i></sub>, Y<sub><i>l</i></sub>) of <i>E</i>, then we define the (<i>k, l</i>)-multiplicity series of any PI-algebra. As an application, we derive from <i>H</i>(<i>E</i>; T<sub><i>k</i></sub>, Y<sub><i>l</i></sub>) an easy algorithm determining the (<i>k, l</i>)-multiplicity series of <i>UT</i><sub><i>n</i></sub>(<i>E</i>).</p>

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Cocharacters of UTn(E)

  • 期刊论文

  • 发表日期：

    2025年6月29日

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  • Lucio Centrone,
  • Vesselin Drensky,
  • Daniela Martinez Correa

摘要

Let F be a field of characteristic 0 and let E be the infinite-dimensional Grassmann algebra over F. In the first part of this paper we give an algorithm calculating the generating function of the cocharacter sequence of the n × n upper triangular matrix algebra UTn(E) with entries in E, lying in a strip of a fixed size. In the second part we compute the double Hilbert series H(E; Tk, Yl) of E, then we define the (k, l)-multiplicity series of any PI-algebra. As an application, we derive from H(E; Tk, Yl) an easy algorithm determining the (k, l)-multiplicity series of UTn(E).