On the wreath product of Schur functions

by 1977- Ingram, Frank

INGRAM III, FRANK. On the Wreath Product of Schur Functions. (Under the direction of Naihuan Jing and Ernie Stitzinger.) The characters of the wreath product G ? Snwere first studied by Specht in [4]. Stanley later proposed the question of certain properties of the wreath product of Schur fucntions with respect to the classical theory of symmetric functions. In this work a relationship is developed between a new power sum symmetric function and the classical power sum symmetric function. Properties for the wreath Schur function are developed from relationships with the classical Schur function and its properties. Finally, a character table is developed that links the new power sum symmetric function with the wreath Schur function. On The Wreath Product of Schur Functions by Frank Ingram III A Dissertation Submitted to the Graduate Faculty of North Carolina State University in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy Mathematics Raleigh 2006 Dr. Naihuan Jing Chair, Advisory Committee Dr. Ernie Stitzinger Co-Chair, Advisory Committee Dr. Tom J. Lada Committee Member Dr. Kailash C. Misra Committee Member Biography Frank Ingram III was born in Ayden, North Carolina on October 12, 1977 to Elsie and Frank Ingram Jr. He is married to Nakisha Ingram of Kinston, North Carolina. He has one son David Jaliyl Ingram. Frank has two sisters and three brothers. They are Angela L. Lloyd, Timothy C. Ingram, Felix H. Ingram, Ron S. Ingram, and Charity L. Ingram. Frank graduated from Ayden-Grifton high school in 1995. He then went on to attend North Carolina Agricultural and Technical State University in Greensboro, NC. He graduated from A & T in 2000, with a Bachelor of Science in Mathematics. Frank began his graduate education at North Carolina State University in the fall of 2000. Frank married his wife Nakisha on July 6, 2002 in Kinston, NC. He received the Master of Science in Mathematics in 2003 from N.C. State. Frank’s son David was born on February 4, 2004. Frank’s team Original Lace’em Up won the basketball graduate faculty championship in March 2005. Frank loves to play basketball, golf, and fish in his spare time. ii