Quantum α-determinant cyclic modules of Uq (gln)

Kazufumi Kimoto, Masato Wakayama

研究成果: Contribution to journalArticle査読

3 被引用数 (Scopus)

抄録

As a particular one parameter deformation of the quantum determinant, we introduce a quantum α-determinant detq(α) and study the Uq (gln)-cyclic module generated by it: We show that the multiplicity of each irreducible representation in this cyclic module is determined by a certain polynomial called the q-content discriminant. A part of the present result is a quantum counterpart for the result of Matsumoto and Wakayama [S. Matsumoto, M. Wakayama, Alpha-determinant cyclic modules of gln (C), J. Lie Theory 16 (2006) 393-405], however, a new distinguished feature arises in our situation. Specifically, we determine the degeneration of the multiplicities for 'classical' singular points and give a general conjecture for singular points involving semi-classical and quantum singularities. Moreover, we introduce a quantum α-permanent perq(α) and establish another conjecture which describes a 'reciprocity' between the multiplicities of the irreducible summands of the cyclic modules generated respectively by detq(α) and perq(α).

本文言語英語
ページ(範囲)922-956
ページ数35
ジャーナルJournal of Algebra
313
2
DOI
出版ステータス出版済み - 7 15 2007
外部発表はい

All Science Journal Classification (ASJC) codes

  • 代数と数論

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