Southern Illinois University Edwardsville SPARK SIUE Faculty Research, Scholarship, and Creative Activity 2015 Kravchuk Polynomials and Induced/Reduced Operators on Clifford Algebras G. Stacey Staples Southern Illinois University Edwardsville,
[email protected] Follow this and additional works at: http://spark.siue.edu/siue_fac Part of the Algebra Commons, and the Discrete Mathematics and Combinatorics Commons Recommended Citation G.S. Staples, Kravchuk polynomials and induced/reduced operators on Clifford algebras, Complex Analysis and Operator Theory, 9 (2015), 445 - 478. http://dx.doi.org/10.1007/s11785-014-0377-z This Article is brought to you for free and open access by SPARK. It has been accepted for inclusion in SIUE Faculty Research, Scholarship, and Creative Activity by an authorized administrator of SPARK. For more information, please contact
[email protected]. Cover Page Footnote The definitive version of this article was published by Springer in Complex Analysis and Operator Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s11785-014-0377-z . This article is available at SPARK: http://spark.siue.edu/siue_fac/6 Kravchuk Polynomials and Induced/Reduced Operators on Clifford Algebras G. Stacey Staples∗ Abstract Kravchuk polynomials arise as orthogonal polynomials with respect to the binomial distribution and have numerous applications in harmonic analysis, statistics, coding theory, and quantum probability. The relation- ship between Kravchuk polynomials and Clifford algebras is multifaceted. In this paper, Kravchuk polynomials are discovered as traces of conjuga- tion operators in Clifford algebras, and appear in Clifford Berezin integrals of Clifford polynomials. Regarding Kravchuk matrices as linear operators on a vector space V , the action induced on the Clifford algebra over V is equivalent to blade conjugation, i.e., reflections across sets of orthogonal hyperplanes.