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Konno, Hitoshi

doi:10.1016/j.geomphys.2009.07.012

Cited by 24 publications

(46 citation statements)

References 53 publications

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“…For K + , let us be in the situation of the proof of Proposition 2.5. From [28,Theorem 4.13] one observes that: for l ∈ Z ≥0 ,…”

Section: Category O and Q-charactersmentioning

confidence: 99%

Baxter operators and asymptotic representations

Felder¹,

Zhang²

2017

Sel. Math. New Ser.

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Abstract. We introduce a category O of representations of the elliptic quantum group associated with sl 2 with well-behaved q-character theory. We derive separation of variables relations for asymptotic representations in the Grothendieck ring of this category. Baxter Q-operators are obtained as transfer matrices for asymptotic representations and obey T Q-relations as a consequence of the relations in K 0 (O).

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“…For K + , let us be in the situation of the proof of Proposition 2.5. From [28,Theorem 4.13] one observes that: for l ∈ Z ≥0 ,…”

Section: Category O and Q-charactersmentioning

confidence: 99%

Baxter operators and asymptotic representations

Felder¹,

Zhang²

2017

Sel. Math. New Ser.

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“…(4.15) Proof. The statement follows from a similar argument to Theorem 4.11 in [31] and E j (1/w)ξ 11···1 = 0 (j = 1, · · · , N − 1),…”

Section: Action Of the Elliptic Currentsmentioning

confidence: 67%

“…We summarize an H-Hopf algebroid structure based on the opposite coproduct to the one used in the previous papers [31,32]. This opposite H-Hopf algebroid structure is used in Sec.4 to construct the finite dimensional representations of E q,p ( gl N ) and U q,p ( gl N ).…”

Section: Acknowledgementsmentioning

confidence: 99%

Elliptic stable envelopes and finite-dimensional representations of elliptic quantum group

Konno

2018

Journal of Integrable Systems

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We construct a finite dimensional representation of the face type, i.e dynamical, elliptic quantum group associated with sl N on the Gelfand-Tsetlin basis of the tensor product of the n-vector representations. The result is described in a combinatorial way by using the partitions of [1, n]. We find that the change of basis matrix from the standard to the Gelfand-Tsetlin basis is given by a specialization of the elliptic weight function obtained in the previous paper [33]. Identifying the elliptic weight functions with the elliptic stable envelopes obtained by Aganagic and Okounkov, we show a correspondence of the Gelfand-Tsetlin bases (resp. the standard bases) to the fixed point classes (resp. the stable classes) in the equivariant elliptic cohomology E T (X) of the cotangent bundle X of the partial flag variety.As a result we obtain a geometric representation of the elliptic quantum group on E T (X).

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“…To construct the deformed vertex operators, one can take an approach that utilizes algebras having the coproduct and that is closely connected with the q-Viraroso/W algebras. There are at least two such algebras: the Ding-Iohara-Miki (DIM) algebras [38,39] and the elliptic algebra U q,p ( g) [40,41,42,43,44,45,46,47]. Here g is an untwisted affine Lie algebra.…”

Section: Introductionmentioning

confidence: 99%

Elliptic algebra, Frenkel–Kac construction and root of unity limit

Itoyama¹,

Oota²,

Yoshioka³

2017

J. Phys. A: Math. Theor.

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We argue that the level-1 elliptic algebra U q,p ( g) is a dynamical symmetry realized as a part of 2d/5d correspondence where the Drinfeld currents are the screening currents to the q-Virasoro/W block in the 2d side. For the case of U q,p ( sl(2)), the level-1 module has a realization by an elliptic version of the Frenkel-Kac construction. The module admits the action of the deformed Virasoro algebra. In a r-th root of unity limit of p with q 2 → 1, the Z r -parafermions and a free boson appear and the value of the central charge that we obtain agrees with that of the 2d coset CFT with para-Virasoro symmetry, which corresponds to the 4d N = 2 SU(2) gauge theory on R 4 /Z

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Elliptic quantum group Uq,p(sl̂

Cited by 24 publications

References 53 publications

Baxter operators and asymptotic representations

Baxter operators and asymptotic representations

Elliptic stable envelopes and finite-dimensional representations of elliptic quantum group

Elliptic algebra, Frenkel–Kac construction and root of unity limit

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