Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials

Feigin, Boris; Jimbo, Michio; Kedem, Rinat; Loktev, S.; Miwa, Tetsuji

doi:10.1215/s0012-7094-04-12533-3

Cited by 19 publications

(45 citation statements)

References 21 publications

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“…The second space (2.6) appears as Example 4 in [FJKLM1]. In the special case M i = δ ik M and M i = δ ik M , (2.6) coincides with the space of coinvariants studied in [FKLMM2,FKLMM3].…”

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 70%

“…Recall that V (k) is an associative unital ring over Z, with basis [l] (0 ≤ l ≤ k) and multiplication rule [FJKLM1]. In this paper we also treat such a generalization for (1.2).…”

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 99%

“…It is rather indirect and consists of several steps. First we apply the general equivalence theorem in [FJKLM1] and reduce the problem to that of a fusion product of finite dimensional sl 2 -modules and their quotient spaces. Each constituent of the fusion product is a reducible sl 2 -module whose cyclic vector is given as a sum.…”

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 99%

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TWO CHARACTER FORMULAS FOR $\widehat{\mathfrak{sl}}_2$ SPACES OF COINVARIANTS

Feigin¹,

Jimbo²,

Loktev³

et al. 2004

Int. J. Mod. Phys. A

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Abstract. We consider sl2 spaces of coinvariants with respect to two kinds of ideals of the enveloping algebra U (sl2 ⊗ C[t]). The first one is generated by sl2 ⊗ t N , and the second one is generated by e ⊗ P (t), f ⊗ P (t) where P (t), P (t) are fixed generic polynomials. (We also treat a generalization of the latter.) Using a method developed in our previous paper, we give new fermionic formulas for their Hilbert polynomials in terms of the level-restricted Kostka polynomials and q-multinomial symbols. As a byproduct, we obtain a fermionic formula for the fusion product of sl3-modules with rectangular highest weights, generalizing a known result for symmetric (or anti-symmetric) tensors.

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“…The second space (2.6) appears as Example 4 in [FJKLM1]. In the special case M i = δ ik M and M i = δ ik M , (2.6) coincides with the space of coinvariants studied in [FKLMM2,FKLMM3].…”

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 70%

“…Recall that V (k) is an associative unital ring over Z, with basis [l] (0 ≤ l ≤ k) and multiplication rule [FJKLM1]. In this paper we also treat such a generalization for (1.2).…”

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 99%

Section: )C[t] ⊕ Ch ⊗ P (T)p (T)c[t] ⊕ Cf ⊗ P (T)c[t] (12)mentioning

confidence: 99%

See 1 more Smart Citation

TWO CHARACTER FORMULAS FOR $\widehat{\mathfrak{sl}}_2$ SPACES OF COINVARIANTS

Feigin¹,

Jimbo²,

Loktev³

et al. 2004

Int. J. Mod. Phys. A

Self Cite

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show abstract

“…While we have proved this in special cases, and did numerical checks in others, a complete verification requires tools beyond the scope of this paper, and will require proving a host of new q-identities. A systematic approach towards a full proof will undoubtedly benefit from a better algebrageometric understanding of the role of K-matrices (see, e.g., [10,20,19,21] for some initial studies).…”

Section: Discussionmentioning

confidence: 99%

K-matrices for 2D conformal field theories

2003

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Abstract. In this paper we examine fermionic type characters (Universal Chiral Partition Functions) for general 2D conformal field theories with a bilinear form given by a matrix of the form K ⊕ K −1 . We provide various techniques for determining these K-matrices, and apply these to a variety of examples including (higher level) WZW and coset conformal field theories. Applications of our results to fractional quantum Hall systems and (level restricted) Kostka polynomials are discussed.

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“…We have a Lemma, which follows from the fact that the fusion product is a quotient of the filtered tensor product (2.11) and a standard deformation argument (Lemma 20 of [7]), [5]:…”

Section: Q-systems Kirillov and Reshetikhinmentioning

confidence: 99%

Proof of the Combinatorial Kirillov-Reshetikhin Conjecture

Francesco

Kedem

2008

International Mathematics Research Notices

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Abstract. In this paper we give a direct proof of the equality of certain generating function associated with tensor product multiplicities of Kirillov-Reshetikhin modules of the untwisted Yangian for each simple Lie algebra g. Together with the theorems of Nakajima and Hernandez, this gives the proof of the combinatorial version of the Kirillov-Reshetikhin conjecture, which gives tensor product multiplicities in terms of restricted fermionic summations.

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Spaces of coinvariants and fusion product, I: From equivalence theorem to Kostka polynomials

Cited by 19 publications

References 21 publications

TWO CHARACTER FORMULAS FOR $\widehat{\mathfrak{sl}}_2$ SPACES OF COINVARIANTS

TWO CHARACTER FORMULAS FOR $\widehat{\mathfrak{sl}}_2$ SPACES OF COINVARIANTS

K-matrices for 2D conformal field theories

Proof of the Combinatorial Kirillov-Reshetikhin Conjecture

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