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SUMMARY:Aspects of Hecke Symmetry
DTSTART;VALUE=DATE-TIME:20181101T090000Z
DTEND;VALUE=DATE-TIME:20181101T100000Z
DTSTAMP;VALUE=DATE-TIME:20190422T164152Z
UID:indico-event-6709@cern.ch
DESCRIPTION:Motivated by their appearance in supersymmetric gauge and stri
ng theories\, we study the relations governing quasi-automorphic forms ass
ociated to certain discrete subgroups of SL(2\,R) called Hecke groups. The
Eisenstein series associated to a Hecke group H(m) satisfy a set of coupl
ed linear differential equations\, which are natural analogues of the well
-known Ramanujan identities for modular forms of SL(2\,Z). We derive these
dentities by appealing to a correspondence with the generalized Halphen s
ystem. Each Hecke group is then associated to a (hyper-)elliptic curve\, w
hose oefficients are found to be determined by an anomaly equation. The Ra
manujan identities admit a natural geometrical interpretation as a vector
field on the moduli space of this curve. They also allow us to associate a
higher- order non-linear differential equation to each Hecke group. These
equations are higher-order analogues of the well-known Chazy equation\, a
nd we show that they are solved by the quasi-automorphic weight-2 Eisenste
in series associated to H(m) and its Hecke orbits\, thereby generalizing a
result of Takhtajan.\n\nhttps://indico.tifr.res.in/indico/conferenceDispl
ay.py?confId=6709
LOCATION: A 304
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=6709
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