Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

Cellularity of a Larger Class of Diagram Algebras

  • BI, N. KARIMILLA (Ramanujan Institute for Advanced Study in Mathematics, University of Madras)
  • Received : 2013.10.03
  • Accepted : 2014.01.29
  • Published : 2015.12.23
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we realize the algebra of ${\mathbb{Z}}_2$ 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 ${\mathbb{Z}}_2$-relations, signed partition algebras and partition algebras.

Keywords

References

  1. J. J. Graham and G. I. Lehrer, Cellular Algebras, Inventiones Mathematicae, 123(1996), 1-34. https://doi.org/10.1007/BF01232365
  2. R. M. Green, Tabular algebras and their asymptotic versions, J. Algebra, 252(1)(2002), 27-64. https://doi.org/10.1016/S0021-8693(02)00002-9
  3. R. M. Green and P. P. Martin, Constructing cell data for diagram algebras, J. Pure Appl. Algebra, 209(2)(2007), 551-569. https://doi.org/10.1016/j.jpaa.2006.07.016
  4. Matthew Bloss, G-colored partition algebras as centralizer algebras of wreath products, Journal of algebra, 265(2003), 690-710. https://doi.org/10.1016/S0021-8693(03)00132-7
  5. M. Parvathi, Signed partition algebras, Comm. Algebra, 32(5)(2004), 1865-1880. https://doi.org/10.1081/AGB-120029909
  6. R. Dipper and G. James, Representations of Hecke algebras of general linear groups, Proc. London Math. Soc., 52(1)(1986), 20-52.
  7. R. Dipper, G. James and A. Mathas, Cyclotomic q-Schur algebras, Math. Z., 229(3)(1998), 385-416. https://doi.org/10.1007/PL00004665
  8. K. Tanabe, On the centralizer algebra of the unitary reflection group G(m, p, n). Nagoya Math. J., 148(1997), 113-126. https://doi.org/10.1017/S0027763000006450
  9. V. Kodiyalam, R. Srinivasan and V. S. Sunder, The algebra of G-relations, Proc. Indian Acad. Sci. Math. Sci., 110(3)(2000), 263-292. https://doi.org/10.1007/BF02878683
  10. C. Xi, Partition algebras are cellular, Compositio Math., 119(1)(1999), 99-109.