Research output: Working paper

**Affinization of category O for quantum groups.** / A. S. Young, C.; Mukhin, E.

Research output: Working paper

A. S. Young, C & Mukhin, E 2012 'Affinization of category O for quantum groups'. <http://arxiv.org/abs/1204.2769>

A. S. Young, C., & Mukhin, E. (2012). *Affinization of category O for quantum groups*. http://arxiv.org/abs/1204.2769

A. S. Young C, Mukhin E. Affinization of category O for quantum groups. 2012 Apr 12.

@techreport{be84192f93c64e939b714fe2de373ef7,

title = "Affinization of category O for quantum groups",

abstract = "Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category O-hat. In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.",

author = "{A. S. Young}, C. and E. Mukhin",

note = "32 pages, latex",

year = "2012",

month = apr,

day = "12",

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Affinization of category O for quantum groups

AU - A. S. Young, C.

AU - Mukhin, E.

N1 - 32 pages, latex

PY - 2012/4/12

Y1 - 2012/4/12

N2 - Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category O-hat. In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.

AB - Let g be a simple Lie algebra. We consider the category O-hat of those modules over the affine quantum group Uq(g-hat) whose Uq(g)-weights have finite multiplicity and lie in a finite union of cones generated by negative roots. We show that many properties of the category of the finite-dimensional representations naturally extend to the category O-hat. In particular, we develop the theory of q-characters and define the minimal affinizations of parabolic Verma modules. In types ABCFG we classify these minimal affinizations and conjecture a Weyl denominator type formula for their characters.

M3 - Working paper

BT - Affinization of category O for quantum groups

ER -