Department of

# Mathematics

Seminar Calendar
for events the day of Wednesday, September 16, 2015.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     August 2015           September 2015          October 2015
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1          1  2  3  4  5                1  2  3
2  3  4  5  6  7  8    6  7  8  9 10 11 12    4  5  6  7  8  9 10
9 10 11 12 13 14 15   13 14 15 16 17 18 19   11 12 13 14 15 16 17
16 17 18 19 20 21 22   20 21 22 23 24 25 26   18 19 20 21 22 23 24
23 24 25 26 27 28 29   27 28 29 30            25 26 27 28 29 30 31
30 31


Wednesday, September 16, 2015

3:00 pm in 345 Altgeld Hall,Wednesday, September 16, 2015

#### T-systems and Representation Theory of Quantum Algebras

###### Bolor Turmunkh (UIUC)

Abstract: T-systems and their combinatorial solutions were introduced in the previous talks. We know T-systems show up in relation to commuting transfer matrices in solvable lattice models, cluster algebras, difference analog of $L$-operators in KP hierarchy, and many more. In this talk, we will discuss T-systems appearing in Representation Theory of quantum affine algebras. In particular, $q$-characters of Kirillov-Reshetikhin modules over quantum affine algebras satisfy the T-system. This result is highly non-trivial and was proved by Nakajima (2003) for types ADE via geometrical construction of quiver varieties and later generalized to all cases by Hernandez. We will introduce the quantum affine algebra $U_q( \widehat{\mathfrak{sl}}_2)$, define $q$-characters, and give some examples. We will then discuss what is known and, more importantly, what is not known about $q$-characters. If time permits, we will broadly introduce $q,t$-characters and the deformed $T$-system they define.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7484073638916016, "perplexity": 368.6130058538996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141182776.11/warc/CC-MAIN-20201125100409-20201125130409-00209.warc.gz"}