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Cellularity of a Larger Class of Diagram Algebras

N. Karimilla Bi
경북대학교 자연과학대학 수학과|2015.12|Kyungpook Mathematical Journal|제55권 제4호|pp. 837-858

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Cellularitypartition algebras
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초록

In this paper, we realize the algebra of Z2 relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of [2]. Using the results of Graham and Lehrer in [1], we give the modular representations of the algebra of Z2-relations, signed partition algebras and partition algebras.

Abstract

In this paper, we realize the algebra of Z2 relations, signed partition algebras and partition algebras as tabular algebras and prove the cellularity of these algebras using the method of [2]. Using the results of Graham and Lehrer in [1], we give the modular representations of the algebra of Z2-relations, signed partition algebras and partition algebras.

참고문헌 (10)

  1. J. J. Graham., "Cellular Algebras", Inventiones Mathematicae, 123, pp.1~34 (1996)
  2. R. M. Green, "Tabular algebras and their asymptotic versions", J. Algebra, 252(1), pp.27~64 (2002)
  3. R. M. Green., "Constructing cell data for diagram algebras", J. Pure Appl. Algebra, 209(2), pp.551~569 (2007)
  4. Matthew Bloss, "G-colored partition algebras as centralizer algebras of wreath products", Journal of algebra, 265, pp.690~710 (2003)
  5. M. Parvathi, "Signed partition algebras", Comm. Algebra, 32(5), pp.1865~1880 (2004)
  6. R. Dipper., "Representations of Hecke algebras of general linear groups", Proc. London Math. Soc, 52(1), pp.20~52 (1986)
  7. R. Dipper., "Cyclotomic q-Schur algebras", Math. Z, 229(3), pp.385~416 (1998)
  8. K. Tanabe, "On the centralizer algebra of the unitary re ection group G(m; p; n)", Nagoya Math. J, 148, pp.113~126 (1997)
  9. V. Kodiyalam., "The algebra of G-relations", Proc. Indian Acad. Sci. Math. Sci, 110(3), pp.263~292 (2000)
  10. C. Xi, "Partition algebras are cellular", Compositio Math, 119(1), pp.99~109 (1999)

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