论文标题
喷气方案，量子Diologarithm和Feigin-Stoyanovsky的主要子空间
Jet Schemes, Quantum Dilogarithm and Feigin-Stoyanovsky's Principal Subspaces
论文作者
论文摘要
我们从JET代数观点分析了Feigin-Stoyanovsky主流代数的主要子空间的结构。对于$ a $ a $级别的主要子空间，我们表明他们的多级希尔伯特系列可以使用量子差异或作为某些生成函数表示``计数``计数''有限维表示。是``经典自由''作为顶点代数。 我们还分析了与Aggine顶点代数$ L_ {1}（\ Mathfrak {so} _5）$，$ L_ {1}（\ Mathfrak {so} _8）$和$ l_1（$ l_1（frak frak {g frak {g} _2）_2）_的无限射流代数相关。我们为$ L_1（\ Mathfrak {so} _5）$的主要子空间提供了一个新的角色公式，证明了它是经典的免费，并提供证据表明，$ L_1（\ Mathfrak {so} _8）$的主要子空间和$ l_1（\ frak {\ frak {\ frak {g} _ {g} _2 _2）
We analyze the structure of Feigin-Stoyanovsky's principal subspaces of affine Lie algebra from the jet algebra viewpoint. For type $A$ level one principal subspaces, we show that their shifted multi-graded Hilbert series can be expressed either using the quantum dilogarithm or as certain generating functions ``counting" finite-dimensional representations of $A$-type quivers. This notably results in novel fermionic character formulas for these principal subspaces. Moreover, our result implies that all level one principal subspaces of type $A$ are ``classically free" as vertex algebras. We also analyze infinite jet algebras associated to principal subspaces of affine vertex algebras $L_{1}(\mathfrak{so}_5)$, $L_{1}(\mathfrak{so}_8)$ and $L_1(\frak{g}_2)$. We derive a new character formula for the principal subspace of $L_1(\mathfrak{so}_5)$, proving that it is classically free, and present evidence that the principal subspaces of $L_1(\mathfrak{so}_8)$ and of $L_1(\frak{g}_2)$ are also classically free.
