Yıl 2017, Cilt 21, Sayı 21, Sayfalar 137 - 163 2017-01-17
| | | |

ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS

Jun Hu [1] , Yabo Wu [2]

264 171

In this paper we investigate certain normalized versions Sk,F (x), Sek,F (x) of Chebyshev polynomials of the second kind and the fourth kind over a field F of positive characteristic. Under the assumption that (char F, 2m + 1) = 1, we show that Sem,F (x) has no multiple roots in any one of its splitting fields. The same is true if we replace 2m + 1 by 2m and Sem,F (x) by Sm−1,F (x). As an application, for any commutative ring R which is a Z[1/n, 2 cos(2π/n), u±1/2 ]-algebra, we construct an explicit cellular basis for the Hecke algebra associated to the dihedral groups I2(n) of order 2n and defined over R by using linear combinations of some Kazhdan-Lusztig bases with coefficients given by certain evaluations of Sek,R(x) or Sk,R(x).

Chebyshev polynomials, dihedral group, Hecke algebras
• [1] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, with
• Formulas, Graphs, and Mathematical Tables, Dover Publications, Inc., New York, 1966.
• [2] G. Benkart and D. Moon, Tensor product representations of Temperley-Lieb
• algebras and Chebyshev polynomials, in: Representations of Algebras and Related
• Topics, in: Fields Inst. Commun., Amer. Math. Soc., Providence, RI, 45 (2005), 57–80.
• [3] A. P. Fakiolas, The Lusztig isomorphism for Hecke algebras of dihedral type,
• J. Algebra, 126(2) (1989), 466–492.
• [4] F. M. Goodman, P. de la Harpe and V. F. R. Jones, Coxeter Graphs and
• Towers of Algebras, Mathematical Sciences Research Institute Publications, 14, Springer-Verlag, New York, 1989.
• [5] J. J. Graham and G. I. Lehrer, Cellular algebras, Invent. Math., 123(1) (1996), 1–34.
• [6] J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies
• in Advanced Mathematics, 29, Cambridge Univ. Press, Cambridge, UK, 1990.
• [7] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke
• algebras, Invent. Math., 53(2) (1979), 165–184.
• [8] J. C. Mason and D. C. Handscomb, Chebyshev Polynomials, Chapman &
• Hall/CRC, Boca Raton, FL, 2003.
• [9] E. Murphy, The representations of Hecke algebras of type An, J. Algebra,
• 173(1) (1995), 97–121.
Konular Makaleler Yazar: Jun Hu Yazar: Yabo Wu
 Bibtex @araştırma makalesi { ieja296263, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2017}, volume = {21}, pages = {137 - 163}, doi = {10.24330/ieja.296263}, title = {ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS}, key = {cite}, author = {Wu, Yabo and Hu, Jun} } APA Hu, J , Wu, Y . (2017). ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS. International Electronic Journal of Algebra, 21 (21), 137-163. DOI: 10.24330/ieja.296263 MLA Hu, J , Wu, Y . "ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS". International Electronic Journal of Algebra 21 (2017): 137-163 Chicago Hu, J , Wu, Y . "ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS". International Electronic Journal of Algebra 21 (2017): 137-163 RIS TY - JOUR T1 - ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS AU - Jun Hu , Yabo Wu Y1 - 2017 PY - 2017 N1 - doi: 10.24330/ieja.296263 DO - 10.24330/ieja.296263 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 137 EP - 163 VL - 21 IS - 21 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.296263 UR - http://dx.doi.org/10.24330/ieja.296263 Y2 - 2016 ER - EndNote %0 International Electronic Journal of Algebra ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS %A Jun Hu , Yabo Wu %T ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS %D 2017 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 21 %N 21 %R doi: 10.24330/ieja.296263 %U 10.24330/ieja.296263 ISNAD Hu, Jun , Wu, Yabo . "ON SOME PROPERTIES OF CHEBYSHEV POLYNOMIALS AND THEIR APPLICATIONS". International Electronic Journal of Algebra 21 / 21 (Ocak 2017): 137-163. http://dx.doi.org/10.24330/ieja.296263