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Brigham Young University

1.
Wagner, David R.
*Schur**Rings* Over Projective Special Linear Groups.

Degree: MS, 2016, Brigham Young University

URL: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7088&context=etd

This thesis presents an introduction to Schur rings (S-rings) and their various properties. Special attention is given to S-rings that are commutative. A number of original results are proved, including a complete classification of the central S-rings over the simple groups PSL(2,q), where q is any prime power. A discussion is made of the counting of symmetric S-rings over cyclic groups of prime power order. An appendix is included that gives all S-rings over the symmetric group over 4 elements with basic structural properties, along with code that can be used, for groups of comparatively small order, to enumerate all S-rings and compute character tables for those S-rings that are commutative. The appendix also includes code optimized for the enumeration of S-rings over cyclic groups.

Subjects/Keywords: Schur rings; association schemes; algebraic combinatorics; projective special linear groups; Mathematics

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Wagner, D. R. (2016). Schur Rings Over Projective Special Linear Groups. (Masters Thesis). Brigham Young University. Retrieved from https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7088&context=etd

Chicago Manual of Style (16^{th} Edition):

Wagner, David R. “Schur Rings Over Projective Special Linear Groups.” 2016. Masters Thesis, Brigham Young University. Accessed October 23, 2020. https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7088&context=etd.

MLA Handbook (7^{th} Edition):

Wagner, David R. “Schur Rings Over Projective Special Linear Groups.” 2016. Web. 23 Oct 2020.

Vancouver:

Wagner DR. Schur Rings Over Projective Special Linear Groups. [Internet] [Masters thesis]. Brigham Young University; 2016. [cited 2020 Oct 23]. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7088&context=etd.

Council of Science Editors:

Wagner DR. Schur Rings Over Projective Special Linear Groups. [Masters Thesis]. Brigham Young University; 2016. Available from: https://scholarsarchive.byu.edu/cgi/viewcontent.cgi?article=7088&context=etd

University of Texas – Austin

2. Mautner, Carl Irving. Sheaf theoretic methods in modular representation theory.

Degree: PhD, Mathematics, 2010, University of Texas – Austin

URL: http://hdl.handle.net/2152/ETD-UT-2010-05-943

This thesis concerns the use of perverse sheaves with coefficients in commutative rings and in particular, fields of positive characteristic, in the study of modular representation theory. We begin by giving a new geometric interpretation of classical connections between the representation theory of the general linear groups and symmetric groups. We then survey work, joint with D. Juteau and G. Williamson, in which we construct a class of objects, called parity sheaves. These objects share many properties with the intersection cohomology complexes in characteristic zero, including a decomposition theorem and a close relation to representation theory. The final part of this document consists of two computations of IC stalks in the nilpotent cones of sl₃and sl₄. These computations build upon our calculations in sections 3.5 and 3.6 of (31), but utilize slightly more sophisticated techniques and allow us to compute the stalks in the remaining characteristics.
*Advisors/Committee Members: Ben-Zvi, David, 1974- (advisor), Distler, Jacques (committee member), Freed, Daniel (committee member), Helm, David (committee member), Rodriquez Villegas, Fernando (committee member).*

Subjects/Keywords: Perverse sheaves; Modular representation theory; Schur-Weyl duality; Parity sheaves; Sheaf theoretic methods; Commutative rings; Decomposition theorem

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Mautner, C. I. (2010). Sheaf theoretic methods in modular representation theory. (Doctoral Dissertation). University of Texas – Austin. Retrieved from http://hdl.handle.net/2152/ETD-UT-2010-05-943

Chicago Manual of Style (16^{th} Edition):

Mautner, Carl Irving. “Sheaf theoretic methods in modular representation theory.” 2010. Doctoral Dissertation, University of Texas – Austin. Accessed October 23, 2020. http://hdl.handle.net/2152/ETD-UT-2010-05-943.

MLA Handbook (7^{th} Edition):

Mautner, Carl Irving. “Sheaf theoretic methods in modular representation theory.” 2010. Web. 23 Oct 2020.

Vancouver:

Mautner CI. Sheaf theoretic methods in modular representation theory. [Internet] [Doctoral dissertation]. University of Texas – Austin; 2010. [cited 2020 Oct 23]. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-943.

Council of Science Editors:

Mautner CI. Sheaf theoretic methods in modular representation theory. [Doctoral Dissertation]. University of Texas – Austin; 2010. Available from: http://hdl.handle.net/2152/ETD-UT-2010-05-943