On factorization results for tensor products and twisted characters [HBNI Th243] (Record no. 60385)
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| 000 -LEADER | |
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| fixed length control field | 02059nam a22002177a 4500 |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240531b |||||||| |||| 00| 0 eng d |
| 041 ## - LANGUAGE CODE | |
| Language code of text/sound track or separate title | eng |
| 080 ## - UNIVERSAL DECIMAL CLASSIFICATION NUMBER | |
| Universal Decimal Classification number | HBNI |
| Item number | Th243 |
| 100 ## - MAIN ENTRY--AUTHOR NAME | |
| Personal name | Sathish Kumar V |
| Relator term | author |
| 245 ## - TITLE STATEMENT | |
| Title | On factorization results for tensor products and twisted characters [HBNI Th243] |
| 260 ## - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT) | |
| Place of publication | Chennai |
| Name of publisher | The Institute of Mathematical Sciences |
| Year of publication | 2024 |
| 300 ## - PHYSICAL DESCRIPTION | |
| Number of Pages | 71p. |
| 502 ## - DISSERTATION NOTE | |
| Degree Type | Ph.D |
| Year degree granted | 2024 |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc | Let An⇥n be a symmetrizable generalized Cartan matrix (GCM) and let g be the associated symmetrizable Kac-Moody Lie algebra with a fixed Cartansubalgebra h. Parabolic Verma modules are highest weight modules for g that simultaneously generalize irreducible integrable modules and Verma modules of g. They are indexed by ( , I) where I ⇢ {1 i n : 2 h⇤ and (↵i_ ) is a non-negative integer}. In the first part of the thesis we give a necessary and sufficient condition for when products of characters of parabolic Verma modules (and their restrictions to some subalgebras of h) are equal. This extends the results of C.S. Rajan [23] and Venkatesh-Viswanath [26] to a class of typically reducible modules. Schur polynomials form a distinguished basis for the ring of symmetric polynomials. The second part of the thesis extends a theorem of Littlewood [16] that asserts that under the action of the map t (which is the adjoint to the map “plethysm by the power sum symmetric function Pt ”) the Schur polynomial s factorizes into a product of t many Schur polynomials indexed by the t-quotients of . More precisely, we generalize this fact to a class of flagged skew Schur polynomials. This includes an interesting family of key polynomials as a special case. As an aside we obtain a family of pattern avoiding permutations that are enumerated by the Fuss-Catalan number. |
| 650 ## - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical Term | Mathematics |
| 690 ## - LOCAL SUBJECT ADDED ENTRY--TOPICAL TERM (OCLC, RLIN) | |
| Topical term or geographic name as entry element | Mathematics |
| 720 ## - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Sankaran |
| Relator term | Thesis Advisor [ths] |
| 720 ## - ADDED ENTRY--UNCONTROLLED NAME | |
| Thesis Advisor | Viswanath |
| Relator term | Thesis Advisor [ths] |
| 856 ## - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | https://dspace.imsc.res.in/xmlui/handle/123456789/879 |
| 942 ## - ADDED ENTRY ELEMENTS (KOHA) | |
| Koha item type | THESIS & DISSERTATION |
| Withdrawn status | Lost status | Damaged status | Not for loan | Current library | Full call number | Accession Number | Uniform Resource Identifier | Koha item type |
|---|---|---|---|---|---|---|---|---|
| IMSc Library | HBNI Th243 | 78039 | https://dspace.imsc.res.in/xmlui/handle/123456789/879 | THESIS & DISSERTATION |